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PHARMACOKINETIC-PHARMACODYNAMIC MODELING OF PIPERACILLIN- 

TAZOBACTAM COMBINATIONS 



By 



TERESA CRISTINA TAVARES DALLA COSTA 



A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL 
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT 
OF THE REQUIREMENTS FOR THE DEGREE OF 
DOCTOR OF PHILOSOPHY 



UNIVERSITY OF FLORIDA 



1996 



Dedicated to my parents Ligia and Dario Dalla Costa. 



ACKNOWLEDGMENTS 



I would like to offer my appreciation and sincere thanks to Dr. Hartmut Derendorf 
for his continuous encouragement since I met him in 1986 in his first official invitation to 
teach pharmacokinetics in my College in Brazil. I think we have come a long way until I 
finally completed this Ph.D. program, and his guidance was always very helpful. I also 
would like to thank the members of my supervisory committee. Dr. Gayle Brazeau, Dr. 
Guenther Hochhaus, and Dr. Kenneth Rand, for their advice and suggestions throughout 
my doctoral research. I would like to specially thank Dr. Hochhaus for his friendship and 
concern about me. 

I would like to thank the secretaries of the Department of Pharmaceutics, in 
particular Mrs. Patricia Khan, for their technical support at all times. I also would like to 
thank Mrs. Marjorie Rigby for helping to keep the laboratory organized and in working 
conditions. 

The completion of the animal experiments for this project was done thanks to the 
help of Dr. Amo Nolting, my fellow graduate student at that time, and Dr. Andreas 
Kovar. I am very thankful for their support. I would like extend my thanks to all 
graduate students who were my colleagues in the "battle front" and will always be my 
friends. Very special thanks to my dear friend Maritza de Cediel, who brought the "Latin 
blood" back to my life and to the laboratory. 



iii 



Apart from the department I would like to thank Prof. Paul Doering and his family 
for giving me and my husband a little taste of the American way of life and a great deal of 
friendship and support. 

Finally I would like to thank my parents for supporting me ever since I can 
remember in everything I tried and in any way they could. A very special thanks to Regis 
who understood how important this project was for me. I could not have received this 
degree without him. 



iv 



TABLE OF CONTENTS 



Eage 

ACKNOWLEDGEMENTS iii 

ABSTRACT viii 

CHAPTERS 

1 INTRODUCTION 1 

Importance of the Study 1 

Hypotheses 4 

2 LITERATURE REVIEW 5 

Piperacillin 5 

P-Lactam Antibiotic and P-Lactamase Inhibitor Combination 9 

Tazobactam 11 

Piperacillin-Tazobactam Combinations 13 

Microdialysis 15 

In vitro Models to Assess Antibacterial Activity 22 

PK-PD Modeling of Antiinfective Agents 33 

3 ANALYTICAL DETERMINATION OF PIPERACILLIN AND 
TAZOBACTAM 39 

Specific Aims of the Analytical Studies 39 

Material and Methods 39 

Drug Assay 39 

Chemicals and Reagents 39 

Instrumentation 40 

TZB Sample Preparation 40 

TZB Chromatographic Conditions 40 

PIP Sample Preparation 41 

PIP Chromatographic Conditions 41 

Assay Validation 4I 

TZB Stability Studies ZZZ'ZZZZi^ 

Results and Discussion 43 



V 



Assay Validation 43 

TZB Stability Studies 44 

Conclusions 45 

4 PHARMACOKINETICS OF PIPERACILLIN AND TAZOBACTAM 
COMBINATIONS 47 

Specific Aims of the Pharmacokinetic Studies 47 

Material and Methods 47 

Experimental Design 47 

Surgical Procedure 48 

Microdialysis Conditions 49 

Microdialysis System and Probe Calibration In Vitro 49 

TZB Protein Binding Determination 50 

Microdialysis Probe Calibration In Vivo 51 

Estimation of Pharmacokinetic Parameters 52 

Statistical Analysis 53 

Results and Discussion 54 

Piperacillin Pharmacokinetics 54 

TZB Probe Calibration In Vivo 56 

Protein Binding Determination 58 

Tazobactam Pharmacokinetics 59 

Conclusions 67 

5 IN VITRO PHARMACODYNAMICS OF PIPERACILLIN AND 
TAZOBACTAM COMBINATIONS 71 

Specific Aims of the Pharmacodynamic Studies 71 

Material and Methods 71 

Drugs 71 

Bacteria 71 

In Vitro Model of Infection 72 

Bacterial Quantification 73 

Comparison Between Human Tissue Levels and In Vitro Levels 73 

Piperacillin Stability In The In Vitro Model 74 

TZB Minimum Effective Concentration 74 

Experimental Design 75 

Results 80 

Comparison Between Human Tissue Levels and In Vitro Levels 80 

Piperacillin Stability In The In Vitro Model 80 

TZB Minimum Effective Concentration 83 

Simulation of Constant Intravenous Infiasion 84 

Simulation of i.v. Bolus Multiple Dosing 89 

Conclusions 99 



vi 



6 PHARMACOKINETIC-PHARMACODYNAMIC MODELING 100 

Specific Aims of the PK-PD Modeling 100 

PK-PD Analysis for Piperacillin alone 102 

Effect of Tazobactam Concentration 105 

Simulation of Constant Infusion 110 

Simulation of i.v. Multiple Dosing 113 

Conclusions 122 

7 FINAL CONCLUSIONS 1 24 

REFERENCES 132 

BIOGRAPHICAL SKETCH 147 



vii 



Abstract of Dissertation Presented to the Graduate School 
of the University of Florida in Partial Fulfillment of the 
Requirements for the Degree of Doctor of Philosophy 

PHARMACOKINETIC-PHARMACODYNAMIC MODELING OF PIPERACILLIN- 

TAZOBACTAM COMBINATIONS 

By 

Teresa Cristina Tavares Dalla Costa 
August, 1996 

Chairman: Hartmut Derendorf, Ph.D. 
Major Department: Pharmaceutics 

The treatment of infections is mainly based on experience rather than on rational 
design. Although some attempts have been made to correlate pharmacokinetic and 
pharmacodynamic parameters of antibiotics in order to predict the outcome of 
antiinfective therapy, the results to date are still not satisfactory. A more detailed 
evaluation of the antimicrobial effect can be obtained by using a pharmacokinetic- 
pharmacodynamic model. Therefore, it was the aim of the present study to model the 
pharmacokinetic and pharmacodynamic data of different combinations of piperacillin, a P- 
lactam antibiotic, combined with tazobactam, a P-lactamase inhibitor, against E. coli in 
order to optimize the dosing regimen for this combination. In the first part of the study, 
the pharmacokinetics of piperacillin and tazobactam alone and in different combinations 
were investigated in rats after single i.v. bolus administration. Total plasma concentrations 
were monitored and microdialysis in the muscle was used to monitor free interstitial 
concentrations. Concentration-time profiles in plasma were adequately described by a 



viii 



two-compartment body model. Predictions of free tissue levels were possible for both 
drugs, alone and in combination, based on parameters derived from plasma data. In the 
second part of the study, free concentrations expected in tissue after i.v. bolus multiple 
dose and constant infusion were calculated based on human pharmacokinetic parameters. 
Escherichia coli ATCC 35218, a P-lactamase producing strain, was exposed to these 
concentrations in an in vitro model of infection. Bacterial counts were monitored for up 
to twenty-four hours. A modified ^^^-^-modd was used to link the pharmacokinetics to 
the pharmacodynamics and describe the number of bacteria as a function of time. The 
resuhs showed a decreased EC50 for piperacillin when combined with TZB in comparison 
to the value obtained for piperacillin alone. The decreased EC50 is a result of 
pharmacokinetic and possibly pharmacodynamic effects. Tazobactam protects piperacillin 
from degradation by the P-lactamase and may also enhance piperacillin's bactericidal 
effect. The comparison of different doses and dosing regimens suggested that as the 
dosing interval is shortened the antiinfective effect can be enhanced. When using a high 
dose of tazobactam, twice a day administration of piperacillin-tazobactam combination 
may be possible. 



ix 



CHAPTER 1 
INTRODUCTION 



Importance of the Study 

The treatment of infections is mainly based on clinical experience rather than on 
rational design. This is because the appropriate selection and use of an antimicrobial agent 
depends on characteristics of the infection, the host, and the drug. Although many 
attempts have been made to correlate all these factors in order to predict the outcome of 
infections the results to date are still not satisfactory for many antibiotics. If one can find a 
way to adjust dose and dosing regimen for treating infections it will be possible to reduce 
the risks of side effects and also the cost of antibiotic therapy. The use of an adequate 
dose and dosing interval from the beginning of the treatment on may reduce the chance of 
development of bacterial resistance which has become a very important issue lately. It can 
also have an impact on patient compliance if it can be shown that less fi-equent 
administration of some of the current antibiotics has the same efficacy as fi-equent and 
rather tedious dosing schedules. An important step in addressing this question is the 
combination of pharmacokinetic parameters of the antibiotic (PK) with its 
pharmacodynamic properties against bacteria (PD) in a PK-PD model. Both parts 
together (PK and PD) can be used to predict the effect as a fimction of time and allow a 
systematic study of interactions between drug and microorganism. By using a PK-PD 
model different doses and dosing regimens can be compared and predictions can be made 
based on a scientific approach. 

It has been reported that the antimicrobial activity of P-lactam antibiotics 
correlates better with the time that plasma concentrations are maintained above the 



1 



2 



minimum antibiotic concentration (MIC) than with any other pharmacokinetic parameter. 
Apparently, once the concentration exceeds a critical value (4-5 times MIC), bacterial 
killing proceeds at zero-order rate, and increasing drug concentrations does not resuh in a 
proportional change in the microbial death rate (1). This critical concentration is easily 
achieved in vivo using current therapy. Furthermore, P-lactam antibiotics do not produce 
a post-antibiotic effect (PAE) in Gram-negative bacteria emphasizing that the presence of 
certain level of the antibiotic is indispensable for the activity (2). This behavior differs 
from that of aminoglycosides, for instance, that exhibit concentration-dependent killing. 
The killing rate of these drugs continues to increase with concentration up to 16-32 times 
the minimum bactericidal concentration (MBC). Since relatively low levels of these 
antibiotics are obtained in vivo compared to their MBCs, a linear relationship between 
dose and bacterial rate can be observed in the therapeutic range. Aminoglycosides also 
produce a concentration-dependent PAE. Combining these two factors one can conclude 
that aminoglycosides show antiinfective activity which is mainly dependent on the initial 
high drug concentrations. P-lactam antibiotics are therefore frequently referred to as 
concentration-independent and time-dependent agents while aminoglycosides are named 
concentration-dependent (3). Since it is known that most of the P-lactam antibiotics have 
a short half-life, more frequent administration of lower doses will result in a better 
antiinfective effect (because it prolongs the exposure of bacteria to the desirable drug 
concentrations) than high doses administered less frequently (for which the high drug 
levels obtained will not translate into a more effective bacterial killing). It was also shown 
in in vitro experiments that for this class of antibiotics the total daily dose can be reduced 
if the dosing interval is increased concomitantly. For the {3-lactam antibiotic piperacillin 
studied in vitro using Escherichia coli, 6 g of the drug given as 1 g six times a day had an 
effect equivalent to 15.6 g given as 5.2 g three times a day (4). The problem associated 
with increasing the number of daily administrations is the decrease in patient compliance 
or the increase in personnel cost for hospitalized patients. 



3 



Bacteria can develop resistance against p-lactam antibiotics mainly by producing 
P-lactamases (5). In order to overcome this resistance, P-lactam antibiotics are frequently 
combined with P-lactamase inhibitors. One of the most effective combinations in this class 
is piperacillin (PIP) and tazobactam (TZB), a P-lactamase inhibitor. For the treatment of 
infections with PIP-TZB combination, it was suggested that the same total daily doses of 
both drugs can be administered less frequently without loss of efficacy (6). In this study 
bacteria were exposed to fluctuating total concentrations of piperacillin alone or in 
combination with tazobactam in an in vitro model of infection which simulates drug levels 
obtained in humans. It was shown that the combination of piperacillin and tazobactam (3 
g/0.375 g) administered four times a day is as effective against P-lactamase producer 
coli as piperacillin and tazobactam (4 g/0.5 g) administered three times a day. However, 
these studies were conducted exposing bacteria to the total drug concentrations observed 
in plasma rather than to the concentrations observed in interstitial fluid which is the most 
common site of infection. It is known that drug concentrations in blood may not reflect 
the concentrations at the cellular level due to the degree of protein binding, capillary and 
membrane permeability, and physico-chemical properties of the drug. 

The suggested efficacy for treatment of infections with PIP-TZB using longer 
dosing intervals opens the possibility of less frequent administration of p-lactam antibiotics 
in humans. However, before any inferences can be made, a more detailed investigation of 
the pharmacokinetic and pharmacodynamic aspects of this combination is necessary. 
Different doses, dose ratios and dosing regimens have to be investigated in simulations of 
achievable free tissue levels. A PK-PD model has to be devised that allows comparison of 
the different doses and dosing regimens investigated. The model can also be used to make 
predictions about the efficacy of doses and dosing regimens of this combination. 



4 



Hypotheses 

The hypothesis for this research project were as follows: firstly, free piperacillin 
and tazobactam tissue concentrations, alone and in combination, can be predicted from 
their respective plasma concentrations based on a diffusion-driven pharmacokinetic model, 
secondly, a pharmacodynamic Ej^ax""^o<^6l can be used to describe the antiinfective effect 
of piperacillin-tazobactam combinations in diff^erent doses, thirdly, in contrast to the 
current recommendations, piperacillin combined with tazobactam can be administered less 
frequently without loss of efficacy, and finally that the possibility of less fi'equent dosing of 
piperacillin combined with tazobactam is not related to changes in piperacillin 
pharmacokinetics but is rather due to the pharmacodynamic effect of the combination. 

In order to test these hypotheses this research project was divided in four parts: 
analytical studies, pharmacokinetic studies, pharmacodynamic studies, and PK-PD 
modeling. Each part is presented in the subsequent chapters. 



CHAPTER 2 
LITERATURE REVffiW 



Piperacillin 

Piperacillin is a semi-synthetic acylureido-penicillin that was developed in 1977 and 
originally referred to as T-1220. The basic structure of piperacillin, like other penicillins, 
is the nucleus with fused P-lactam and thiazolidine rings (7). Piperacillin's chemical name 
is [25-[2a,5a,6p(^*)]]-6-[[[[(4-ethyl-2,3-dioxo-l-piperazinyl)carbonyl]- 
amino]phenylacetyl]amino]-3,3-dimethyl-7-oxo-4-thia-l-azabicyclo-[3.2.0]heptane-2- 
carboxylic acid (8). The presence of an intact P-lactam ring is essential for its antiinfective 
activity. The ureido structure in the side chain provides the diverse physico-chemical and 
biological properties of PIP compared to other penicillins (Figure 2-1). The pKg of 
piperacillin is 4.14. The pH of an aqueous solution of piperacillin sodium is 5.5-7.0 (8). 
The pH range of highest stability is 4-6. The sodium salt of PIP is highly water soluble 
(714 g per 1 L). 

Piperacillin is not absorbed from the gastrointestinal tract and has to be 
administered either intravenously or intramuscularly. PEP pharmacokinetics has been 
described by either a one-compartment (9-10) or a two-compartment body models (11). 
After intravenous administration in humans, piperacillin kinetics is characterized by high 
maximum plasma concentrations, a small volume of distribution, a short half-life and a 
rapid decay in plasma concentrations (12). After intravenous bolus administrations of 15, 
30, and 60 mg/kg mean peak plasma concentrations in healthy volunteers were 102 
Hg/mL, 232 ng/mL, and 522 ng/mL, respectively (11). 



5 



6 




COOH 

Tazobactam Tazobactam Metabolite Ml 

Figure 2-1. Chemical structures of piperacillin, 7V-desethyl piperacillin, tazobactam, and 
tazobactam metabolite (Mi). 



Piperacillin 4 g given by infusion over 30 min to healthy subjects results in a mean peak 
concentration of 244 |ig/mL (9). Intramuscular injection of 0.5 g and 2 g resulted in 70 to 
80% bioavailability . Peak concentrations were reached within 45 min and averaged from 
5.13 to 30 \ig/mL, respectively (13). 

PIP apparent volume of distribution at steady state (Vdgs) averaged 30.5 L after 1 
g dose, 27.5 L after 2 g, and 21.2 L after 4 g administered as i.v. bolus injection (14). 
The volume of distribution for the elimination phase (Vdarea) is also dose-dependent (15). 
After intramuscular injection of 1 g of piperacillin the Vdarea obtained was 38.6 L/1.73m2 
(15). 

Total body clearances after both intravenous and intramuscular administration 
decreased with increasing PIP dose: 24.52 L/h and 12.58 L/h after intravenous doses of 1 
g and 6 g, respectively (15). In patients with normal renal fiinction PIP is primarily 
eliminated via the kidneys (80%) by glomerular filtration and tubular secretion. Most of 



7 



the given dose, 60 to 80%, is recovered unchanged in the urine. The percentage of 
recovery is lower after i.m. than after i.v. administration of the drug (15). Average renal 
clearances of 245.7 mL/min and 186.9 mL/min are reported after 1 and 6 g doses, 
respectively (15). The renal clearance exceeds the glomerular filtration rate by far, 
suggesting that tubular secretion is the major factor affecting the dose-dependent behavior 
shown by piperacillin (1 1). Less than 1% of the dose is metabolized to A^-desethyl- 
piperacillin, an active metabolite (8) (Figure 2-1). About 20% of the dose is excreted 
through the biliary tract producing concentrations in the bile up to forty times of those in 
the serum (16-17). 

Serum half-lives are slightly dose-dependent with values ranging from 0.6 to 1.05 
h after i.v. bolus administration of 1 and 6 g, respectively (15). After i.m. injection the 
half-lives are higher (1.2 h for 1 g and 1.3 h for 6 g of PIP). The prolongation of half-life 
with increasing dose is not clinically significant (9). 

Piperacillin protein binding is approximately 21% (9-10). This relatively low 
protein binding explains the extent with which PIP diffuses into tissues and other body 
fluids. Therapeutic concentrations of piperacillin are achieved in a variety of tissue and 
body fluids including cerebrospinal fluid, bronchial mucosa, kidney, bone, subcutaneous 
tissue, peritoneal fluid, heart tissue, aqueous humor, gallbladder wall and female genital 
tissue (13, 16, 18-23). Penetration into the amniotic fluid is not as high as that into the 
umbilical cord, and passage into the breast milk is negligible (13). 

Piperacillin pharmacokinetics is altered in children, pregnant women and elderly 
subjects. The elimination half-life is shorter in children than in adults (24). It was also 
shown that the younger the child the shorter the half-life. The total body clearance in 
infants (1 to 6 months) was also lower than in older children (5 to 10 years) (25). In 
children, the mean renal clearance of the drug represented 63% of the total body clearance 
suggesting a substantial non-renal route of elimination for piperacillin (24-25). In elderly 
subjects the total clearance of PIP is reduced by 15% and the volume of distribution is 



8 



increased by 43% compared to young adults. As a result the mean residence time of PEP 
in the body is doubled in elderly subjects (2.09 ± 0.15 h) compared to young adults (1.15 
± 0.04 h) (26). Larger volumes of distribution and higher clearance rates are observed for 
piperacillin during pregnancy. Thus, higher doses may be required for effective treatment 
of serious infections in pregnant women near the term (27). 

The elimination half-life of piperacillin is increased from 60 min in normal patients 
to 96 min in patients with mild renal insufficiency (creatinine clearance 50 to 80 mL/min). 
With moderate renal failure (creatinine clearance 1 5 to 50 mL/min) it increases to 
approximately 130 min and reaches 150 min in patients with severe renal insufficiency 
(creatinine clearance 9 to 15 mL/min), Then, the diminution of kidney function to less 
than one-tenth of the normal value is accompanied by only a 3 -fold increase of the 
elimination half-life of piperacillin (28). The urinary recovery of PIP decreases with the 
degree of renal insufficiency from approximately 80% of the dose in normal subjects to 
practically zero in patients with end-stage renal insufficiency (29). The non-renal or biliary 
clearance probably compensates for the renal elimination in renal compromised patients 
(29). In renal impaired patients undergoing hemodialysis the half-life of PIP is decreased 
on average 60.5% compared to patients not undergoing dialysis (30). This confirms that 
piperacillin can readily be removed by dialysis. A dose reduction or an increased interval 
between doses is indicated according to the degree of renal impairment. Doses must also 
be adjusted to account for a reduced renal clearance between hemodialysis treatment as 
well as for removal of the drug during hemodialysis (29). 

Piperacillin is a bactericidal drug that demonstrates a broad spectrum of 
antibacterial activity (9, 31). The mechanism of action is related to its effect on the 
bacterial cell wall. In Gram-negative microorganisms, PIP binds covalently to the penicillin 
binding proteins (PBP) located between the layers of the cell membrane. The PBP are 
enzymes that constitute the system responsible for the synthesis of the bacterial cell wall. 



9 



The cell wall is responsible for the shape and integrity of the bacteria. Piperacillin 
has a high degree of affinity to PBP 3, which is important for the bacterial cell division, to 
PBP la and lb, responsible for the cell wall integrity and to PBP 2, responsible for the cell 
wall shape (5, 32). At low concentrations piperacillin produces bacterial filamentation 
without any lytic activity (33). Cell lysis occurs at high concentrations without any 
appreciable filamentation. 

Piperacillin demonstrates a wide range of antibacterial activity against Gram- 
positive and Gram-negative aerobic and anaerobic organisms. It is effective against 
Proteus, Enterobacter, Serratia and Actinobacter species. It exhibits good activity 
against clinical isolates of Pseudomonas, Proteus, Klebsiella, Serratia, Bacteroides and 
Emerococci. Haemophilus influenza and Neisseria gonorrhoeae also have demonstrated 
a marked sensitivity to piperacillin (13). 

B-Lactam Antibiotic and |3-Lactamase Inhibitor Combination 

Bacterial resistance have rendered some of the older P-lactam antibiotics obsolete. 
The antibacterial effect of P-lactam antibiotics depends on their capacity to resist or avoid 
the barriers opposed by the bacteria (5). There are three mechanisms by which bacteria 
resist the action of P-lactam antibacterial agents: production of enzymes that mediate 
antibiotic degradation, alteration of outer membrane permeability, and decreased 
penicillin-binding protein affinity (34). Three classes of enzymes can hydrolyze p-lactam 
antibiotics: p-lactamases, acylases, and esterases (5). p-Lactamase mediated hydrolysis of 
the P-lactam nucleus is the most common and important mechanism of bacterial resistance 
to P-lactam antibiotics. P-Lactamases are produced by some Gram-positive and all Gram- 
negative bacteria (12). Gram-negative bacilli produce both chromosomally encoded and 
plasmid-encoded p-lactamases (5). For Gram-positive bacteria only the production of p- 
lactamase and the alteration of the PBP affinity are available mechanisms of resistance 



10 



because of the location of the PBP on the exterior surface of the cytoplasmic membrane 
(35). The PBP on Gram-negative bacteria are located in the inner membrane. The 
antibiotic has to cross the outer membrane and avoid the enzymatic degradation at the 
periplasmic space in order to reach its target. For these microorganisms the interplay 
between the permeability of the outer membrane (OM) and the degradation rate by the P- 
lactamase is very important (36). If the antibiotic penetrates the OM slowly and the 
enzymatic activity is low, sufficient drug concentration can build up in the periplasmic 
space to bind to the PBP. For an agent that penetrates faster, the concentration in the 
periplasmic space approaches that in the external medium unless a very fast inactivation 
process occurs inside the cell. Thus, for most agents the decisive factor is not the absolute 
rate of OM penetration but the balance between the penetration rate and the subsequent 
inactivation rate. The difference in |3-lactam concentration on either side of the OM 
depends on these two factors (37). In general 3-lactam agents cross the OM through 
porin channels. Diffusion of some agents is limited by molecular weight and electrostatic 
charges; difflision of others is limited by bulky substituents on the acyl side chain of the p- 
lactam nucleus (38-39). Two outer membrane proteins (Omps) have been identified and 
characterized for E. coli. (OmpF and OmpC). The difference between the two proteins is 
the diameter of the channel. The bacteria can mutate to produce only OmpC (narrowest 
diameter) in order to resist to the penetration of P-lactams (40). 

The co-administration of a non-antimicrobial drug capable of inhibiting p- 
lactamase activity in conjunction with a P-Iactam antibiotic is a strategy that has been used 
to overcome P-lactamase-mediated resistance. The inactivation of the P-lactam antibiotic 
by the P-lactamase and the inhibition of the p-lactamase by the P-lactamase inhibitor can 
occur in a competitive, non-competitive, or terminal (suicide) fashion (41). Competitive 
inactivation involves the formation of a reversible enzyme-inhibitor or enzyme-antibiotic 
complex. Even though the enzyme complex is reversible, the bacteria can be killed if the 
enzyme is bound long enough for the antibiotic to bind to PBP and initiate the lethal 



11 



effect. Non-competitive inhibition is progressive and time dependent. This mechanism 
does not seem to be viable for either of the drugs in combination. Suicide inhibition 
resuhs in the formation of a stable acylated complex between the P-lactamase and the 
inhibitor. The product can be either a hydrolyzed inhibitor and a reactivated enzyme or an 
inert complex. Although the reaction may be in fact reversible in some situations, the 
enzyme is complexed for such a long period of time that, for all practical purpose, the 
reaction is permanent. All P-lactam inhibitors clinically used up to now are irreversible 
inhibitors of the P-lactamases (42). 

Two P-lactam inhibitors widely used are sulbactam, co-administered with 
ampicillin, and clavulanic acid, used in combination with ticarcillin. Piperacillin has been 
introduced recently combined with tazobactam to treat infections caused by P-lactamase 
producing bacteria. 

Tazobactam 

Tazobactam (TZB) is a P-lactamase inhibitor from the class of penicillanic acid 
sulfones developed by R.G. Micetich and Taiho Pharmaceutical Company (Tokushima, 
Japan) and originally referred to as YTR-830 (43). TZB's chemical name is [25- 
(2a,3P,5a)]-3-methyl-7-oxo-3-(l//-l,2,3-triazol-l-ylmethyl)-4-thia-l-azabicyclo- 
[3.2.0]heptane-2-carboxylic acid (Figure 2-1). The pKa of TZB is 2.1 and hence it is 
ionized in tissues and body fluids except in the acidic conditions of the stomach (8). TZB 
is very soluble in water (500g of the sodium sah dissolves in 1 L of water). 

Tazobactam has inhibitory activity against Richmond and Sykes types II, III, IV, 
and V P-lactamases, staphylococcal penicillinase and extended-spectrum P-lactamases. All 
these enzymes are plasmid encoded (34). Tazobactam also has activity against class Ic 
chromosomally-mediated enzymes, but limited activity against other class I enzymes. It 
acts as an irreversible inhibitor against the major P-lactamase classes. Unlike clavulanic 



12 



acid, TZB has only weak to moderate enzyme inducing activity (44). TZB seems to be 
more effective than sulbactam and clavulanic acid in inhibintig some of the most common 
plasmid encoded P-lactamases like TEM-1, TEM-2 and SHV-1 enzymes (45). 
Tazobactam binds to PBP 2 of Gram-negative organisms but its antibacterial activity is 
negligible (46). 

Tazobactam has been shown to extend the spectrum of activity of piperacillin 
against bacteria producing both chromosomal and plasmid-mediated 3-lactamases (34, 47- 
50). Piperacillin-tazobactam possesses a broad spectrum of activity including Gram- 
positive and Gram-negative aerobic and anaerobic organisms (51). Gram-negative 
bacteria include many Enterobacteriaceae and Pseudomonas aeruginosa. Susceptible 
Gram-positive bacteria include Enterococcus fecalis. Listeria monocytogenes and 
streptococci. This combination has good activity against Bactericides fragilis and other 
anaerobes (34). Piperacillin-tazobactam is, overall, the most active p-lactam-p-lactamase 
inhibitor combination as demonstrated by in vitro studies (52-53). It is recommended for 
the treatment of polymicrobial infections (54). Decreased susceptibility to piperacillin- 
tazobactam is observed in organisms with more than one mechanism of resistance (34). 

Tazobactam pharmacokinetics investigated in humans over the dose range of 0. 1 
to 1 .0 g was found to be typical of those for other p-lactam (8, 12) (Table 2-1). The 
maximum plasma concentrations obtained at the end of an infusion were approximately 
proportional to the dose administered. As the dose was increased, total clearance 
decreased and, consequently, the AUG rose more than proportionally to the dose 
administered. The volume of distribution for the lowest dose (0. 1 g) is approximately 
13 L and increased by 20% for the highest dose (1 g). The amount of TZB excreted 
unchanged by the kidney increased from 60.3% to 77.0% over the dose range studied. 
The half-life increased significantly with dose. Tazobactam is metabolized by cleavage of 
the p-lactam ring to produce the metabolite Mi (Figure 2-1) which is further broken down 
to a butanoic acid derivate. On average, 26% of the dose is transformed to Mi which has 



13 



13 



no P-lactamase activity; the metabolism is suggested to take place predominantly in the 
hepatocytes (8). The protein binding of ^^C-tazobactam in human plasma by 
ultrafiltration was found to be 20-23% over a concentration range of 1-100 [ig/mL (8). 

Piperacillin-Tazobactam Combinations 

The effect of co-administration of piperacillin and tazobactam on the 
pharmacokinetic behavior of each of these agents was investigated for combinations of 
PIP-TZB 2 gk^^iV'SSih g and 4 g/0.5 g (8, 12, 34). The pharmacokinetics of 
piperacillin remained unaffected after co-administration with tazobactam in a ratio 1 :4 and 
1 :8 (8). The pharmacokinetics of TZB, on the other hand, was significantly affected by 
the presence of PIP. A summary of these results is shown in Table 1. The plasma 
concentrations and the half-life of TZB were increased after co-administration with 
piperacillin when compared to TZB administration alone. The half-life of TZB when 
administered in combination is similar to the half-life of PIP and the plasma levels of the 
two compounds parallel one another. The changes observed in TZB pharmacokinetics 
when administered in combination are related to the fact that both drugs are eliminated by 
tubular secretion and since PIP was given in an 8: 1 ratio, there is a competitive inhibition 
for transport at the renal site in favor of piperacillin. 

Renal elimination of tazobactam and piperacillin accounts for 50-60% of the dose 
after combined administration (8). Since piperacillin and tazobactam are eliminated 
primarily through the kidneys their dosage may be adjusted according to the renal 
fiinction. The administration of PIP and TZB to patients with compromised renal fiinction 
showed that reduction in creatinine clearance has a greater effect on the total clearance of 
tazobactam than on that of piperacillin (55). This is because in normal healthy volunteers 
the renal excretion of unchanged TZB is higher than that of PIP. However the difference 
between changes in total clearance of TZB and PIP are not of sufficient magnitude to 



14 



Table 2-1. Pharmacokinetic parameters of tazobactam in healthy volunteers after 
administration alone and in combination with piperacillin (means and CV). 





INO. 01 


Infusion 


n 

^max 


ATir"/-! 

AUCO-QO 




Vdss 


Half 


unnary 






liiliC 


(man \ 


^mg n/L; 


^llil_//illlll^ 


K'-') 


lllC 


CACl CllUll 






1 tnin 1 
^^1 1 1111^ 










W 




T7Ti n 1 
U. 1 


A 




e c 

J.J 


A 1 


416 


iZ.o 


U. JJ 






















T7R n 9S 


"I 
J 




14 


1 1 7 
11./ 


J JO 


1 J . 1 


v/.tj 


71 n 

/ 1 .u 








(23) 


(12) 


(11) 


(8) 


(7) 


(7) 


TZB 0.5 


4 


30 


23.5 


20.8 


415 


14.6 


0.44 


70.9 








(15) 


(20) 


(24) 


(12) 


(17) 


(5) 


TZB 1.0 


3 


30 


51.0 


53.5 


327 


15.8 


0.63 


77.0 








(6) 


(29) 


(26) 


(11) 


(32) 


(9) 


PIP 2/ 


8 


5 


16.2 


12.4 


339 


23.2 


0.88 


65.7 


TZB 0.25 






(24)a 


(11) 


(11) 


(6) 


(31) 


(16) 


PIP 4/ 


6 


30 


34.4 


41.4 


202 


12.6 


0.78 


55.4 


TZB 0.5 






(6) 


(4) 


(4) 


(7) 


(9) 


(14) 



Adapted from Sorgel and Kinzig (1993) (8) 
^Estimated concentration at the end of 5 min infusion 



warrant adjustment of the dose of tazobactam independent of that of piperacillin (55). 
Thus, in renal failure the dosage of this combination should be adjusted in the same 
manner as adjustments are made for piperacillin alone in renal compromised patients. 

An injectable combination product containing piperacillin sodium and tazobactam 
sodium was approved by the FDA in 1994 (56-57). This product is available from Lederle 
Laboratories under the name of Zosyn®. Zosyn® is supplied in two different 
combinations: PIP and TZB 1:4 (2 g/0.5 g or 3 g/0.375 g) or PIP and TZB 1:8 (4 g/0.5 
g). The combination product is indicated for the treatment of moderate to severe infection 
caused by P-lactamase-producing strains of microorganisms that are resistant to PIP alone 
but are susceptible to the combination of PIP and TZB. Specific indications include 
appendicitis and peritonitis caused hyE. coli, or Bacteroides spp.; uncomplicated and 
complicated infections of the skin and skin structure caused by Staphylococcus aureus; 
post-partum endometritis and pelvic inflammatory disease caused by E. coli; and moderate 
cases of community acquired pneumonia caused by Haemophilus influenzae. The dosage 



15 



regimen for this combination varies according to the type and severity of the infection 
treated. The dosage of PIP-TZB most commonly recommended in aduhs and children 
(>12 years) with severe infections is 4/0.5 g every 8 hours. For patients who have mild to 
moderate infections the recommended dose is 2/0.5 every 8 hours (51). 

Microdialysis 

The antibiotic concentrations in plasma are indirectly related to the cure of 
infections. Only the free drug concentrations present at the site of infection are 
responsible for the antiinfective effect. The antibiotics have to distribute from the blood 
into the infected tissue in order to be active against microorganisms. Only the free, 
unbound fraction of the antibiotic is capable of passing through capillary fenestrations and 
can be available to interact with bacteria. Hence, the determination of plasma 
pharmacokinetics must be conducted together with the determination of free levels of the 
drug in the tissue. Monitoring free antibiotic concentrations in tissue was done in the past 
using different techniques that were volume-demanding and traumatic such as fibrin clots, 
tissue chambers and skin blister (58-59). These techniques can alter the normal 
distribution patterns of the drug in the tissue. Also, due to the large volumes involved, 
often times rapid changes in concentrations could not be measured with these techniques. 

Microdialysis is a sampling technique which offers some advantages for 
pharmacokinetic studies. First, no physiologic disturbance is produced in the investigated 
tissue allowing the determination of actual free drug levels observed in normal conditions. 
Second, many samples can be withdrawn from the same experimental animal in acute or 
chronic experiments since the technique does not produce animal fluid loss. Third, the 
method provides the ability to monitor pharmacokinetics in several organs at the same 
time using a single experimental animal. Finally, no sample preparation is required prior to 
the analysis of the compound of interest. Microdialysis gives direct access to the 



16 



extracellular fluid in many tissues. For the study of drugs acting on cell surface bound 
structures or on extracellular structures such as enzymes or microorganisms, direct access 
to the biophase free levels of the drug is obtained (60). 

Microdialysis is a technique for measurement of unbound concentrations of 
compounds present in the tissue interstitial space that was introduced in 1966 for use in 
experimental brain research (61). Many additional contributions were made over the years 
in investigations of changing endogenous substance levels due to diseases or special 
conditions as well as in monitoring free levels of administered drugs. Microdialysis has 
been used to investigate other tissues besides brain such as muscle, adipose and 
subcutaneous tissue, liver, lungs, kidneys, and blood in a variety of experiments with 
different species of animals in anesthetized or conscious conditions (62-67). The 
technique, first restricted to animals, has also been applied to humans. In human studies 
endogenous substances such as glycerol (68), amino acids (69) and glucose (70) were 
monitored. The pharmacokinetics of exogenous compounds like propranolol (71), 
caffeine (72), ethanol (73), acetaminophen and gentamicin (74) have been investigated in 
humans by using this technique. Microdialysis in humans was performed in subcutaneous 
(68, 70-71, 73,75) and adipose tissues (72), skin (73), muscle (74), and brain (76). The 
use of microdialysis as a clinical tool has been reported for the monitoring of plasma levels 
of lactate, pyruvate, glucose, creatinine, urea, adenosine, inosine, and hypoxantine in 
intensive care patients (77). A method for routine monitoring of disturbances in brain 
energy metabolism in patients in the neurosurgical intensive care unit by using 
intracerebral microdialysis was also investigated (78). 

The potential use of microdialysis in pharmacokinetic studies is not restricted to 
the determination of drug concentrations in tissue. This technique can be used to monitor 
changes in protein binding of drugs by directly investigating blood levels over a period of 
time after drug administration in vivo (79). It can also be used for the determination of 
protein binding in vitro. It has been shown that the results obtained with microdialysis are 



17 



similar to the ones obtained using ultrafiltration for a number of drugs (80). Microdialysis, 
however, is not suitable for all compounds, due to their physico-chemical properties and 
analytical limitations (81). 

The microdialysis technique uses the dialysis principle and consists of a membrane 
permeable to water and small solutes which is continuously flushed on one side with a 
solution devoid of the substance of interest, whereas the other side faces the interstitial 
space. A concentration gradient is created causing diffusion of substances from the 
interstitial space into the dialysis probe. The continuous flow through the probe carries 
substances to the sampling site for further analysis (61). These samples are devoid of 
proteins and can be directly analyzed. On-line analysis of drugs can be performed by 
combining microdialysis with mass spectrometry (82) or other analytical equipment such 
as capillary eletrophoresis or HPLC. 

The microdialysis probe can be of two types having the inlet and outlet tubes in a 
serial arrangement or positioned in parallel. The pore size of the dialysis membrane 
determines the molecular weight cut off" of the compounds entering the probe (83). 

The perfusion fluids used for flushing the microdialysis probe vary widely with 
respect to composition and pH, depending on the tissue studied. However, they should 
always be isotonic with plasma and mimic as much as possible the composition of the fluid 
surrounding the tissue under investigation (61, 84). 

Since microdialysis is performed under sink conditions, a true equilibrium between 
perfusate solution and interstitial space concentrations will never be reached. However, 
the concentrations of drugs in the dialysate are proportional to the true free interstitial 
concentrations. For quantitative analysis, it is necessary to determine the relative recovery 
of the microdialysis probes for specific conditions and drugs. The relative recovery is 
defined as the ratio between the concentration in the dialysate and the concentration of the 
substance outside the probe (83). 



18 



The relative recovery is influenced by factors such as temperature, perfiision flow 
rate, dialysis membrane area and composition, time after the beginning of the perfusion, 
and diffijsion coefficient (61, 83). The relative recovery obtained for different substances 
using the same microdialysis probe is known to vary. This may be due to difference in the 
molecular weight and consequently differences in diffusion coefficients. Furthermore, the 
difiusion coefficients are known to increase with temperature increasing consequently the 
recovery. For this reason determinations of recovery in vitro should always be performed 
at temperatures identical to the tissue (37 ° C). 

The perfusion flow rate is inversely proportional to the relative recovery. 
Increasing the flow rates proportionally decreased the drug concentration in the dialysate. 
A compromise has to be achieved between the flow rate and the limit of quantification of 
the analytical method used. Flow rates between 1 and 5 ^g/mL are generally acceptable. 

The in vitro performance of the microdialysis probe depends on the characteristics 
of the semipermeable membrane. Polyacrylonitrile membranes have the highest extraction 
in vitro. However, the performance in vivo does not differ significantly for the different 
kinds of membranes available (85). The explanation for this finding is that the main factor 
limiting extraction in vitro is the membrane resistance to diffusion, whereas in vivo, tissue 
resistance to diffusion is the limiting step. In conclusion, in vitro measurements of 
microdialysis probe extraction are not a reliable way of calibrating //; vivo performance. 
As expected, relative recovery is directly proportional to the size of the dialysis membrane 
area. By increasing the membrane area, lower concentrations can be detected using 
reasonable perfijsion flow rates. The increase in membrane area, however, is limited by 
the size of the tissue or organ under investigation. 

The relative recovery is time dependent (61). Initially, the recovery is high but it 
rapidly decreases. This is probably due to a steep concentration gradient across the 
dialysis membrane when the probe is first inserted into the tissue. The gradient gradually 
declines due to the drainage of the immediate vicinity of the membrane. After perfusion of 



19 



the probe for about one hour this constitutes a minor factor (< 1%) and can be neglected 
for practical purposes (83). 

The relative recovery can be determined in vitro and in vivo. The in vitro recovery 
is used to estimate the in vivo value. However, the recovery determined in vitro generally 
overestimates the free concentration in tissues. This occurs because diffusion rate in 
tissues is usually smaller than diffusion in vitro due to tortuosity and limited volume 
fraction of the extracellular space (86-88). Hence, the evaluation of the correlation 
between in vitro and in vivo recoveries is fundamental in order to accurately determine the 
free tissue concentrations. 

The most common techniques used for the determination of in vivo recovery are 
the extrapolation to zero flow rate method, the point of no net flux method, the slow 
perfusion rate method, and the internal reference method (89). 

The extrapolation to zero flow rate method was developed in 1985 by Jacobson 
and co-workers (90). This method is based on the relationship between recovery and flow 
rate. If the tissue concentration is kept constant due to a continuous i.v. infusion of the 
drug, changes in perfusion flow rate will produce proportional changes in the relative 
recoveries obtained. The free tissue concentration can be estimated by nonlinear 
regression to a set of dialysate concentrations measured at different flow rates. The in 
vivo recovery is calculated as the dialysate concentration obtained for one specific flow 
rate divided by the tissue concentration estimated by nonlinear regression. 

The point of no net flux method was developed by Lonnroth and co-workers in 
1987 (75). The method is based on determining mass transport of the analyte across the 
microdialysis membrane as a function of perfusate concentration. The experiment is 
performed under steady-state conditions obtained by constant i.v. infusion. When the 
concentration of the analyte is lower in the perfusate than in the external media, the 
direction of diffusion is from the media into the probe. The situation is reversed when the 
concentration is higher in the perfusate, in which case the analyte diffuses out of the probe 



20 



to the external media. The point of no net flux is the condition at which external and 
internal concentrations are equal. This point can be determined by linear regression of the 
net transport for different perfusate concentrations. Net transport across the membrane is 
calculated by subtracting the concentration of analyte recovered in the dialysate from the 
concentration that was added to the perfusate solution. The slope of the linear regression 
line is equal to the relative recovery. This method is considered by some authors to be one 
of the most adequate and precise methods to determine true interstitial concentrations (91- 
93). The disadvantage of this method, as well as of the previous one described, is the 
amount of time necessary to calibrated the probe. For four different flow rates or four 
different concentrations in the perfiisate solution at least 8 to nine hours of experiment are 
needed for the calibration of a single probe. This fact limits the application of these two 
methods as a routine calibration procedure for every microdialysis probe. 

The slow perfusion rate method was proposed by Menacherry and co-workers in 
1992. The method is based on the fact that at very slow perfusion rate the concentration 
of analyte in the dialysate is near equilibrium with the external concentration (91). While 
theoretically it would require zero flow rate for concentrations to equilibrate, in practice 
better than 90% efficiency is obtained at slow perfusion rates around 50 nL/min. The in 
vivo concentration estimated at this very low rate is used to establish the relative recovery 
at other flow rates. Although this method is less time consuming than the other two 
described previously, some major drawbacks are associated to it such as: lack of sufficient 
sample for analysis, sample evaporation during long collection times, and difficulties in 
obtaining a reliable constant flow rate. 

The three methods described so far require the calibration of the microdialysis 
probe previous to the actual experiment to determine the pharmacokinetics of the drug 
under investigation. Retrodialysis is a method that allows for continuous assessment of 
recovery in vivo during the study period (94-95). Retrodialysis involves the measurement 
of diffusive loss of molecules (retrodialysis calibrator or internal standard) from the 



21 



perfusate solution into the environment surrounding the probe, under sink conditions. The 
drug under investigation and the calibrator should have similar physico-chemical 
properties to assure similar diffusion characteristics. The relative loss, by analogy to the 
relative recovery, is the ratio of calibrator concentration difference between perfusate and 
dialysate over the perfusate concentration. A similar concept was developed in 1991 by 
Scheller and Kolb for the internal reference method (96). In this approach the calibrator is 
the labeled form of the compound of interest. Both methods assume that the diffusion of 
the analyte across the microdialysis membrane is not ahered by the diffusion of the 
calibrator and vice- versa. Retodialysis (74) and the method of no net flux (71) have been 
used for in vivo probe calibration in human experiments. 

Free tissue concentrations of P-lactam antibiotics were investigated by 
microdialysis by Deguchi and co-workers (69). The purpose of the study was to 
demonstrate the rapid equilibration between vascular and extravascular concentrations of 
free drug. Two P-lactam antibiotics were investigated in rats: SY5555, a penem 
antibiotic, and cefminox, a cephalosporin. Total tissue levels for lung, muscle and liver 
were determined and compared with free levels determined by microdialysis. The resuhs 
showed that total levels can vary significantly according to the type of tissue investigated. 
The free tissue levels, however, were similar for all three different tissues studied. The 
results illustrate that total drug levels should not be used to compare or design dosing 
regimens since they do not reflect the active concentrations at the site of action. 

In a study using piperacillin alone some of the issues related to use of microdialysis 
for determination of free tissue concentrations were addressed (97). It was shown that the 
microdialysis probe recovery is constant for different external concentrations and that the 
probes are capable of responding swiftly to changes in the outside concentrations. It was 
also shown that under the investigated conditions PIP relative recovery in vitro was 
equivalent to the in vivo recovery determined in rat muscle using the point of no net flux 
method. Therefore, for piperacillin the in vitro recovery could be used as a good 



22 



approximation of the in vivo recovery. The pharmacokinetic results from the study 
demonstrated that piperacillin concentration-time profiles after i.v. bolus administration 
can be fitted to a two compartment body model. The distribution of the drug between 
central and peripheral compartments is a diffusion driven process. Finally, it was shown 
that free concentrations in the interstitial fluid measured by microdialysis can be predicted 
from pharmacokinetic parameters of the drug estimated from plasma data. 

In summary, the knowledge of free drug concentrations at the site of action is very 
important for pharmacodynamic studies since it is the free drug that exerts the 
pharmacological effect. Pharmacological effects based on total plasma levels would be 
overestimated because the pharmacologically inactive fraction of the drug is also being 
considered. Microdialysis allows for the investigation of free tissue levels of drugs 
without disturbing the physiological conditions. Its application to pharmacokinetic studies 
has a great potential. The use of free drug levels in a PK-PD model should result in better 
predictions of the bactericidal effect for different doses and dosing regimens compared to 
the predictions obtained using total drug concentrations. 

In vitro Models to Assess Antibacterial Activity 

Unlike other diseases, the causative agent of many infections can be isolated from 
the patient and its interaction with drugs can be studied in vitro (98). The efficacy of 
antibiotics studied in vitro does not necessarily translate into efficacy in patients. On the 
other hand, comparisons of treatments for bacterial infections in patients is difficult 
because outcomes are a fijnction of multiple variables related to the microorganism, drug 
administered and patient general conditions. The use of volunteers for this type of study is 
limited for ethical reasons. The use of animal models has also been investigated. The 
drawback of animal models is the fact that they do not often truly reflect human 
pharmacokinetics. Pharmacokinetic parameters like volume of distribution, elimination 



23 



rates or protein binding may vary considerably among species. Elimination half-lives of 
most antibiotics are much shorter in animals than in humans (99). Therefore, animal 
models may suggest optimal dosing regimens for antibiotics that are not applicable to 
human therapy. 

Several in vitro models have been developed over the years in an attempt to 
determine antiinfective activity of single or combined drugs, to compare doses and dosing 
regimens, to compare new and older drugs, and to optimize therapy in preclinical studies. 
Iw vitro models can closely mimic infections observed in neutropenic patients because they 
permit the study of interactions of bacteria and antibiotic without the presence of host 
defense. In vitro models of infections offer some advantages over animal models in the 
study of antibiotic efficacy. In these models many variables that occur during treatment 
can be independently evaluated. Effect of dosing, pharmacokinetics and culture conditions 
can be analyzed outside the host (99). Furthermore, the use of in vitro models may reduce 
the number of animals required for drug dosage investigations. 

Commonly used parameters to quantify the activity of antibiotics against a certain 
bacteria are the minimum inhibitory concentration (MIC), the minimum bactericidal 
concentration (MBC), and the minimum antibiotic concentration (MAC). The MIC is 
defined as the minimum concentration that prevents visible growth, i.e., zero net change in 
the number of organisms over time. The MIC only estimates the growth inhibition and its 
efficacy in vivo relies on the host immune system to eradicate the pathogen. The MBC is 
the minimum antibiotic concentration that kills 99.9% of the original number of bacteria. 
Hence, the MBC reflects not only the antibiotic ability to inhibit growth but also its killing 
effect. It is used to assess antiinfective activity in clinical situations where the host 
immune system is less effective in eradicating the pathogen, such as endocarditis, 
osteomyelitis, meningitis, and infections in neutropenic patients (2). The MAC is the 
smallest concentration found in vitro that exhibits any influence on the rate of growth of 
bacteria when compared with control cultures without antibiotic. The MAC may be many 



24 



times lower than the MIC proving the assumption that the MIC value is a threshold for 
antibiotic bacterial activity is not valid (2). 

When the MIC and the MBC of an antibiotic have similar order of magnitude the 
agent is called bactericidal. Drugs included in this class are p-lactam antibiotics, 
aminoglycosides, and quinolones. When the antibiotic does not produce a reliable 
bactericidal effect at concentrations close to the MIC it is called bacteriostatic. In this 
situations the MBC can largely exceed the MIC. Examples of this class are macrolides, 
tetracyclines, and chloramphenicol. Because the MBC is not routinely determined, 
bacteriostatic drugs are avoided when treating infections where bactericidal activity is 
required (2). The MIC, the MBC, and the MAC are determined under standardized 
conditions using constant drug concentrations. However, the constancy of drug levels 
does not reflect the in vivo situation where the bacteria are exposed to fluctuating 
concentrations due to the metabolism and elimination in the body. For this reason, some 
in vitro systems were developed in order to simulate more closely the in vivo conditions 
and to better characterize the antiinfective effect. 

The in vitro models can be divided into three groups according to the way drug 
concentrations are investigated: the first group investigates the bacterial behavior under 
constant concentration of the antibiotics, the second group simulates changing drug 
concentration by means of dilution, and the third group uses diflusion or dialysis as the 
mechanism to simulate fluctuating antibiotic concentrations. Since the MIC only reflects 
the bacterial activity at one specific concentration and time (18-24 h), some investigators 
studied the antibacterial effect of bacteriostatic and bactericidal drugs by exposing bacteria 
to constant drug concentrations and collecting samples at specific intervals over a period 
of time (100-102). From the killing curves obtained (in presence of drug) compared to the 
control (growth rate curves), it was possible to mathematically describe the activity of the 
antibiotic. Any change in the normal first-order growth rate constant observed in the 
absence of the drug would be due to the presence of the antibiotic and will produce a new 



25 



apparent growth rate constant for the bacteria (kapp). These apparent growth rate 
constants for bacteriostatic antibiotics were described mathematically and classified into 
four classes according to Garrett (103). Class I interactions describe antibiotic activity 
using a linear relationship between kapp and drug concentration. In Class II interactions 
the apparent growth rate (kapp) decreases with increasing drug concentration to 
asymptotically approach zero. Class III interactions are characterized by a Class I 
behavior at low antibiotic concentrations and decreasing rates of change in kapp at higher 
concentrations. Class IV interactions show S-shaped plots of kapp vs. drug concentration 
probably due to drug binding to nutrients at low concentrations. 

For bactericidal drugs (such as |3-lactam antibiotics) the kapp may assume negative 
values because killing is induced above certain concentrations. The killing rate shows a 
linear relationship with the difference between the actual drug concentration and the 
minimum drug concentrations necessary to produce effect (104). The killing effect shows 
a lag time due to the relatively slow onset of full bactericidal activity presented by these 
antibiotics. Mattie and co-workers (105-108) used another mathematical approach to 
describe the observed effect. Growth curves in the presence of antibiotic were described 
as a quadratic function of time, with initial growth rates and killing rates as concentration- 
dependent variables. Since the growth rate is assumed constant, the killing rates depend 
only on drug concentration. 

Although it was possible to mathematically describe the effect of antibiotics against 
bacteria when exposed to constant concentrations, the correlation of this result to the in 
vivo situation was not possible. In clinical treatment of infections in patients, bacteria are 
exposed to continuously changing antibiotic concentration. Various designs of /w vitro 
models have been proposed to expose bacteria to changing antiinfective concentrations. 
These models try to simulate the concentration-time profiles of antibiotics using 
pharmacokinetic parameters of the drug observed in humans. 



26 



The simplest technique used to simulate the continuous change in concentration 
patterns which occurs in vivo is the stepwise dilution. In these experiments bacteria are 
exposed to drug concentrations which approximate the concentration-time curves in 
human serum seen during clinical therapy. The bacterial inoculum is incubated with an 
antibiotic concentration that is kept constant for a while, then diluted according to the 
half-life of the drug, incubated again and so on. The smaller the dilution step the closer 
the model simulates the drug elimination profile observed in vivo. The bacteria can either 
be diluted with the dilution steps used for the drug (109) or remain undiluted due to use of 
fihers (4). Stepwise dilutions are time consuming. On the other hand, the technique is 
simple to perform and does not require pumps to simulate different concentration profiles. 

A model that reproduced more closely the serum kinetics of the antibiotics was 
first described by Sanfilippo and co-workers in 1968 (1 10). In this model, a dose of the 
antibiotic was injected into the culture flask when bacterial inoculum was in the log- 
growth phase. Sterile plain broth solution was pumped at a fixed rate into the flask, 
diluting the antibiotic in a linear fashion. The volume of the culture flask increased during 
the experiment causing the dilution of the antibiotic as well as the bacterial inoculum. This 
dilution method is able to simulate any concentration-time profile, however when the 
difference between peak and trough is 10 to 100-fold within one dosing interval, the 
culture volume has to be expanded in the same way, which creates a practical problem. 

Grasso and co-workers described in 1978 a one-compartment open model that 
simulated the pharmacokinetics of drugs after intravenous administration (111). The same 
dilution method was used as described previously. Two flasks were connected by tubing 
to a peristaltic pump. From the reservoir flask sterile broth solution was pumped at a 
constant rate into the flask that contained bacteria and drug. The flask that contained the 
culture was connected to a vessel to collect the excess fluid resulting fi-om the dilution. 
The antibiotic concentrations decreased exponentially in the culture flask simulating the 
half-life of the antibiotic in human serum. The initial antibiotic concentration in the system 



27 



was calculated to mimic the peak concentration of the drug expected for the dose under 
investigation. Grasso also introduced a modification of this model in order to simulate 
first order absorption kinetics as it would be obtained after oral or intramuscular 
administration (111). In this model, a third flask that contains the antibiotic solution was 
placed between the reservoir of plain broth solution and the culture flask. The antibiotic 
solution is pumped into the culture flask simulating the absorption rate constant of the 
drug. The concentration in the culture flask increases until a maximum when it equals the 
concentration in the antibiotic flask. Eventually the concentration in the culture flask 
decreases exponentially. Bergan and co-workers introduced a modification of the method 
by adapting a photometer in the path of the antibiotic-bacteria mixture to continuously 
measure the bacterial level by turbidity (112-114). In this way the bacterial plating and 
counting for determination of colony forming units (CFU) was not necessary. These 
dilution models, with small modifications, were used by several investigators (115-117). 
Ledergerber and co-workers modified the Grasso model by introducing computer drive 
control to apply the appropriate antibiotic infiasion rate and to record the turbidity (117). 
The major drawback of these dilution methods is that the bacterial inoculum is diluted 
with the antibiotic. When the dilution rate constant is lower than the bacterial growth 
rate, the growth curve does not differ substantially from that observed in a static situation 
(111). However, when the dilution rate is higher than the bacterial growth rate the 
artificially increased bacterial clearance has to be taken into account. Some authors have 
proposed equations to mathematically correct the bacterial count (118-119). It is 
important to mention that the effect of dilution can be corrected mathematically only if the 
cultures are increasing or decreasing exponentially. 

In order to overcome the bacterial dilution problem some authors modified the 
one-compartment model to include a filter that keeps the bacteria within the cell culture 
(120). Al-Asadi and co-workers proposed the use of two glass tubes connected by a 
cellulose acetate membrane (121). One tube had the bacteria in the log-growth phase and 



28 



the other tube had the antibiotic solution. The antibiotic is allowed to diffuse into the 
compartment containing the bacteria. To reverse the diffusion process, broth solution was 
pumped into the compartment containing the culture. This created a flow of broth across 
the membrane into the antibiotic-containing compartment from which accumulated broth 
was continuously removed by a second pump. Because of the flow across the membrane 
the half-life of the drug could be simulated and the bacterial inoculum remained essentially 
constant. The disadvantage of using filters is that they tend to clog after some time due to 
the presence of increasing inoculum or debris produced by the bacteria multiplication 
making it difficult to control a constant infusion rate using pumps (99). 

All the models described so far simulate the elimination of the drug following a 
monoexponential profile. However, some antibiotics show a short distribution phase 
followed by a longer elimination phase. To closely mimic the biexponential decline of 
serum kinetics following intravenous administrations Murakawa and co-workers 
introduced a two compartment model that utilizes a bi-directional flow between the central 
and peripheral compartments (122). At the beginning of the experiment antibiotic and 
bacteria are placed into the central compartment. Due to continuous mixing of the 
contents of the central and peripheral compartment, as well as dilution of the central 
compartment with plain broth solution, a biexponential decline of the drug in the central 
compartment is achieved. Bacteria are diluted out of the central compartment into the 
peripheral compartment and out of the system. The dilution of the bacterial inoculum has 
to be corrected mathematically. 

In the one-compartment model bacteria are exposed to serum concentration-time 
profiles observed in humans. However, except for septicemia, the site of infection is the 
tissue water. It is more relevant then to simulate concentration-time profiles that mimic 
those observed in interstitial fluid or tissue rather than in serum. The diffusion models are 
basically two-compartment models. The bacteria are kept at constant inoculum in the 
"tissue" compartment and the drug is diluted in the "central" compartment simulating the 



29 



half-life of the antibiotic. A membrane is used to separate the two compartments. The 
antibiotic has to diffuse from the "central" to the peripheral "compartment" simulating in 
this way the build up as well as the elimination of the drug in the tissue. Using the 
diffusion principle several models were described in the literature (123-127). The main 
problem with some of these models were the large volumes that were necessary in order 
to reproduce the kinetics of the drug. A more sophisticated model was devised by Blaser 
and co-workers in 1985 (128). The extravascular infection sites are represented by 
artificial capillary units which contain the bacterial cultures within the peripheral 
compartments. The capillary unit consists of a plastic shell through which runs a bundle of 
1 50 artificial capillaries. The capillaries are hollow fibers of polysulfone with porous walls 
acting as membranes. The peripheral compartment interfaces with the central 
compartment through the porous capillary walls which allow for bi-directional penetration 
of antibiotics but prevent the passage of bacteria. Bacteria are placed into the outer 
chamber of the capillary unit. Several capillary units are placed in series and are connected 
with plastic tubing to the central compartment which consists of the central reservoir plus 
the lumen of the capillaries and the tubing connecting the units. The antibiotic is 
administered into the central compartment. The antibiotic-broth is continuously pumped 
through the capillaries and penetrates into the peripheral chambers containing bacteria. 
Sterile plain broth is continuously pumped into the central compartment at a flow rate set 
to simulate the elimination half-life of the drug in humans. The volume of the central 
compartment remains constant but the concentration changes over time. The volume of 
the peripheral compartment is in general 10 mL. Samples are withdrawn from the 
peripheral compartment for bacteria counting. This model can be used to simulate 
continuous and intermittent administration of drugs (129). It can be also used to simulate 
oral or intramuscular administration of an antibiotic by inserting an absorption chamber 
before the central compartment (130). One of the main advantages of this model is the 
possibility of studying combinations of antibiotics with different half-lives (131-136). 



30 



More specific models were developed over the years in order to simulate in vivo 
conditions observed in special infection sites. Some examples of these models are the 
artificial bladder model (137), the model used to simulate acute otitis media (138), and the 
in vitro pharmacodynamic model of endocarditis (139). To study the treatment of 
infections in implants in vitro models were devised to investigate the activity of 
antimicrobials not only on suspended bacteria but also on the biofilm formed by adherent 
bacteria (140-141). 

Although some in vitro models were designed considering the fact that most of the 
infections occur in the interstitial fluid, few investigators realized that only the free 
concentration present in the tissue is available to produce antiinfective effect. The first 
researcher to address the problem of protein binding in in vitro infection models was Lintz 
(142). This author derived equations to predict total and free tissue concentrations and 
showed that in vitro simulations of total plasma concentrations and even total tissue 
concentrations would expose the bacteria to much higher levels of the antibiotics than 
those obtained in interstitial fluid. This could explain why some in vitro predictions of 
activity did not correspond to the clinical outcome observed in patients (142). To what 
extent protein binding affects the antibiotic activity is an issue for discussion. Some 
authors consider that only protein binding higher than 80% can cause a significant 
difference in the drug activity (143). Some experiments in vitro showed that differences in 
the effect time course can be observed between simulations of total serum concentrations 
and free interstitial concentrations for the same antibiotic even when the protein binding is 
lower than 80% (116). The results of a study to determine the importance of extracellular 
protein binding with highly protein-bound drugs suggested that the onset of antibacterial 
effect for this kind of drugs is delayed in the presence of proteins in the site of infection. 
On the other hand, a more prolonged effect after the cessation of the treatment can be 
observed since drug concentrations tend to decline more slowly under these conditions 



31 



(144). How these differences observed in vitro affect the in vivo outcome of infections is 
still to be determined. 

Few experiments were design to assess the host defense mechanisms in the 
presence of oscillating drug concentrations against bacterial cultures. Shah studied the 
activity of imipenem against Gram-negative bacteria using human blood as culture media 
instead of broth solution (145). The effect of enoxacin against S. aureus in the presence 
or absence of leukocytes was studied by Blaser and co-workers using the two- 
compartment capillary model (99). The presence of leukocytes increased bacterial killing 
ten times after the first two hours but no significant difference was observed after six 
hours. Leukocyte administration was more effective when given after six hours of 
antibiotic administration. These findings are consistent with more recent studies showing 
enhanced leukocyte killing against resistant bacterial subpopulations which were selected 
during exposure to aminoglycosides and quinolones in conventional in vitro experiments 
(146). The mechanism by which preexposure to antibiotics influences leukocyte bacterial 
killing is not clear although potentiation of opsonization is a possibility (146). The 
increased leukocyte activity seems to be linked to bacterial resistance. Subinhibitory 
concentrations of antibiotics can induce morphological and biochemical changes in 
bacteria which might render these organisms more vulnerable to leukocytes. These 
resistant organisms should not represent a problem to the immune competent hosts. 
However the use of aminoglycosides alone in immune compromised patients may not 
result in successful therapy. Conventional in vitro models do not address these kind of 
problems because in general they test the antibiotic effect in the absence of host defense 
which represents a greater challenge to their antibacterial activity compared to the in vivo 
situation. However, the example illustrates the importance of careful analysis of the in 
vitro results when making extrapolations to in vivo situations. 

The result of the in vitro experiment is the determination of viable bacteria as a 
function of time and the influence of the antibiotic administered on the microorganism 



32 



kinetics. Different methods can be used to follow bacteria multiplication or death. The 
turbidity method relies on the good correlation between the optical density of a suspension 
and the number of particles per unit volume (113). A refinement of this approach is to use 
a Couher counter to count the actual number of particles. Both methods are not very 
reliable because the number of particles counted may not represent the number of viable 
microorganisms. Furthermore, it is not clear whether the change in the form of the 
bacteria that have been exposed to antibiotics results in a change in their optical qualities 
(108). To overcome this problem it was suggested that the total living bacterial cell mass 
could be estimated by measuring the intracellular adenosine triphosphate (ATP). 
Although this method has been used for measuring the effect of antibiotics on bacterial 
growth some data published showed that antibiotics profoundly affect the ATP content of 
live microorganisms (108). Because of this consideration the counting of the live 
microorganism as colony forming units (CFU) remains the more reliable method for 
determining bacterial viability in the presence of bactericidal drugs (108) whereas the 
photometry is a suitable alternative when studying bacteriostatic agents (113). 

The in vitro models discussed here simulate infections in neutropenic patients and 
can be used for preclinical studies with antibiotics, studies of optimal dosing and dosing 
regimen, effect of specific factors like protein binding and post-antibiotic effect as well as 
antibiotic combinations. These models cannot replace the in vivo animal models or the 
clinical investigation of antibiotic activities, but they allow a reduction of such experiments 
and may complement assessment of antibiotic activity. Discrepancies between in vitro and 
in vivo results may be due to numerous causes: differences in bacterial growth rate in vitro 
and in vivo, difference in medium composition and limitation of some substract for 
bacterial growth in vitro, the fact that in vitro experiments bacteria are floating in the 
medium in opposition to some in vivo situation where bacteria can adhere to implants or 
other structures, differences in temperature maintained for the in vitro studies, changes in 
the morphology and physiology of the microorganism in order to adapt to the in vitro 



33 



conditions among others (147). One has always to keep in mind that the in vitro models 
of infection are very useful to investigate the interaction between bacteria and antibiotic 
but extrapolation of the results to in vivo situations has to be made with great care. 

An in vitro model was devised in our group to study the pharmacodynamic effect 
of piperacillin alone against E. coli following administration of constant or fluctuating 
concentrations (4). A one-compartment in vitro model was used to simulate only the free 
interstitial concentrations obtained in humans after different doses and dosing regimens. 
The free tissue concentrations were estimated based on human plasma pharmacokinetics. 
To simulate drug elimination, broth solution containing piperacillin and the bacteria was 
withdrawn through sterile filters and replaced by free sterile broth. In this way the 
antibiotic half-life was simulated in a stepwise fashion. The number of bacteria was not 
affected by the withdrawal of samples due to the use of the sterile filter. The number of 
viable cells was determined by counting the CFU after overnight incubation. This in vitro 
model will be used for this project in order to allow the comparison of different dosing 
regimens of PIP and TZB. 



PK-PD Modeling of Antiinfective Agents 

The appropriate selection and use of an antimicrobial agent is based on 
characteristics of the infection, the host, and the antiinfective agent (148). Important 
features of the infection are the characteristics of the infecting agent and its susceptibility 
to the antimicrobial agent. Important information about the host are the site of infection, 
the host immune status and the host's general ability to absorb and metabolize drugs. 
With respect to the drug two aspects have to be considered: its pharmacokinetic 
properties such as absorption , distribution into the infected tissues, and elimination, and 
its pharmacodynamic features such as mechanism of action, the cidal or static nature of the 
antimicrobial effect and the rate at which it occurs. An approach that incorporates all 



34 



these factors in designing the best therapy is currently not available. An important step in 
this direction is the combination of the pharmacokinetic and pharmacodynamic properties 
of the antibiotic in order to predict the outcome of a specific therapy. 

The pharmacokinetic parameters used to characterize the time course of the 
antibiotic concentration in plasma include the area under the curve (AUC), the peak 
concentration and the half-life. The duration of time that the plasma concentration 
exceeds a threshold value, generally the MIC, is also used (t > MIC). The AUC, the peak 
level over MIC and the t > MIC are dose and dosing interval dependent parameters. For a 
given total daily dose the AUC over 24 h is independent of the administration schedule. 
The same daily dose given at longer dosing intervals will resuh in larger peak/MIC ratios 
but smaller t > MIC periods of time. The opposite will occur when smaller doses are 
administered more frequently. The difference observed with different dosing schedules 
will be most marked with drugs with short half-lives. 

As discussed previously, parameters commonly used to quantify the activity of 
antiinfective agents are the MIC and the MBC. These measurements of activity are 
inadequate to completely characterize an antibiotic's pharmacodynamic properties because 
they reflect the net drug effect following a fixed time of incubation . The result is often 
viewed as a yes or no phenomena: growth vs. no grov^h, killing vs. no killing. These 
parameters do not account for the time course of the antimicrobial activity. 

Another pharmacodynamic parameter used to describe the activity of antibiotic 
after its removal from the in vitro system is the postantibiotic effect (PAE) (149). It is 
defined as the delay in bacterial regrowth which occurs as a result of transient antibiotic 
exposure after the removal of the antimicrobial (2). The PAE is observed with almost all 
antibiotics. However, not all antimicrobial agent produce a PAE with all microorganisms. 
In general, antibiotics for which the mechanism of action is related to protein synthesis or 
inhibition of DNA or RNA synthesis exert PAE with most bacteria. Some examples are 
aminoglycosides, quinolones and chloramphenicol. Inhibitors of cell wall synthesis such as 



35 



P-lactams antibiotics may produce PAE with some Gram-positive stains, but rarely 
produce PAE with Gram-negative bacteria. The PAE is considered an important 
parameter in designing dosing regimens. The presence of PAE for an antibiotic implies 
that the infrequent dosing resulting in temporary very low levels of the drug is possible 
without compromising drug efficacy. 

Based on these pharmacokinetic and pharmacodynamic parameters and 
experimental results from animal and in vitro studies the antibiotics are generally referred 
to as concentration-dependent or time-dependent agents (3). When the contribution on 
the killing process is more affected by increasing the peak/MIC ratio than by prolonging 
the exposure time of the bacteria to the antibiotic, the antiinfective agent is called 
concentration dependent (150). These antibiotics have relatively long PAEs. The 
relationship observed between efficacy and the period that the drug concentration remains 
above the MIC (t > MIC) is less significant than the pronounced killing effect observed 
with high dose. The antibiotics in this group are aminoglycosides and fluoroquinolones. 
In an attempt to maximize the peak/MIC ratio, the concept of once a day administration 
for aminoglycosides has evolved (151). Avoidance of toxicity provides additional 
incentive for less-frequent administration of aminoglycosides (152). 

Some antiinfective agents such as |3-lactmas and vancomycin appear to have a 
different bacterial killing profile. Apparently when the concentration exceeds a critical 
value 4 to 5 times the MIC), killing proceeds at zero order rate, and increasing drug 
concentration does not result in a proportional change in the microbial death rate (3). 
These antibiotics are called concentration-independent or time-dependent. For them the 
most important PK-PD relationship is the t > MIC. If the dosing interval for these drugs 
is short in relationship to their half-lives, the t > MIC will be maximized, as will bacterial 
eradication. Some strategies for achieving this goal are using frequent dosing of the 
antibiotic or administering the antibiotic by continuous infusion (153-154). The 
applicability of constant infusion as the optimal method for the administration of p-lactam 



36 



antibiotics has to be clinically investigated with respect to emergence of bacterial 
resistance, incidence of side effects and patient outcome (154). The prediction of the best 
antibiotic dosing interval by adding up the expected t > MIC (based on the dose and the 
antibiotic pharmacokinetics and the MIC) and the PAE (when quantifiable) was also 
suggest in the literature (155). 

Although the PK-PD correlations are used presently to better dose antibiotics 
(156), the approaches are still more descriptive than predictive of the antiinfective activity. 
An attempt to obtain a general method to optimize the dosing schedules for the treatment 
of infections with P-lactam antibiotics, quinolones or aminoglycosides was proposed by 
Schentag and co-workers (157). They postulated a target value of 125 h for the area 
under the inhibitory curve (AUIC) over 24 hours. The AUIC can be easily calculated as 
the ratio of 24-hours AUC (for time points with respective concentrations above the MIC) 
and the MIC. In a systematic evaluation of this approach we showed that different serum 
concentration profiles can result in the same AUIC although some of the dosing regimens 
are known to be ineffective (158). We also derived a precise equation for the calculation 
of AUIC and showed that for the situation when the trough concentration at the end of the 
dosing interval equals the MIC, the AUIC is independent of the MIC, dose and drug 
concentration in serum and it is determined only by the half-life of the drug, the time of 
infusion and the dosing interval. Consequently, it does not seem valid to accept any single 
AUIC target breakpoint for the dosing of antibiotics in these three classes investigated. 

The need to devise a better approach to compare and optimize antibiotic doses and 
dosing regimens is obvious. An important contribution to this end is the combination of 
pharmacokinetics and pharmacodynamic properties of the antibiotic in a PK-PD model. 
By using this approach more detailed information can be obtained about the time course of 
the antimicrobial effect. A systematic comparison of different dosing regimens can be 
obtained and predictions can be made about the efficacy of treatments prior to clinical 
testing. 



37 



Pharmacokinetic/pharmacodynamic modeling is used to describe the effect of a 
dmg as a function of time, where the pharmacokinetic part gives information about the 
concentration-time profile of the drug in the body, and the pharmacodynamic part offers 
information about the concentration-effect relationship. The known relationship between 
dose, concentration of the drug in plasma, and drug effects may be used as a starting point 
in dosage individualization. 

Some of the pharmacodynamic models described in the literature are the fixed- 
effect model, the linear model, the log-linear model, the Eax-model and the sigmoid-Emax" 
model (159). These models can also be used as a starting point to develop more complex 
and sophisticated structures in order to describe the data. The fixed effect model is that 
where the observed effect is either present or absent. The degree of the effect is not 
important, rather the critical element is whether or not the effect occurs. The linear model 
describes an effect that is directly proportional to drug concentration. This model, 
however, lacks the ability to define the maximum effect. The log-linear model describes 
an effect that is directly proportional to the log of the concentration. It has the same 
restrictions as the linear model. The E^^^ -model is the simplest model that describes 
drug effect over the whole range of concentrations by a hyperbolic relationship. This 
model has two important properties: it predicts the maximum effect a drug can achieve 
and it predicts no effect when drug is absent. The sigmoid-Emax -model is a variation of 
the Emax-model where the effect/concentration curve cannot be described by a simple 
hyperbolic form. In this case a parameter has to be added to the traditional En^ax-^odel 
to account for the different slopes of the curve. 

The most common approach to link the PK and PD parts of the model is usually 
the use of an effect compartment (160). This approach assumes that the drug enters and 
leaves the effect site by first order process. Using this approach the effect compartment is 
allowed to float during the fitting process to make both data sets match ("soft link") (161). 
Another approach described is the "hard link" model which allows a true prediction of the 



38 



pharmacodynamic data based on the pharmacokinetic data and information from in vitro 
studies (161) (bacterial killing rates in this case). In this way, the pharmacodynamic data 
is not used for the characterization of the model but it is predicted. A further and 
important step when using this approach is to validate the model with pharmacodynamic 
data obtained from studies with patients. 

A modified En^ax-i^odel was derived to describe the bactericidal effect of 
piperacillin against E. coli in vitro simulations of free fluctuating concentrations expected 
in human tissue after i.v. bolus administration (4). A set of parameters were derived which 
allowed the simulation of the bactericidal effects of any given dose or dosing regimen. 
The same model will be investigated to describe the antimicrobial effect of PEP-TZB 
combinations in the present study. 



CHAPTER 3 

ANALYTICAL DETERMINATION OF PIPERACILLIN AND TAZOBACTAM 



Specific Aims of the Analytical Studies 

The specific aims of the analytical studies were to develop a sensitive and specific 
assay to quantify tazobactam in rat plasma and in microdialysis dialysate, and to study the 
stability of tazobactam in different media: water, phosphate buffer, rat plasma, rat plasma 
filtrate, and Muller-Hinton Broth solution (MHB) in the presence and absence of E. coU 
ATCC 25922. 

Material and Methods 

Drug Assay 

The assay for determination of TZB in biological fluids by HPLC was developed 
based on previously published procedures (162-163). The HPLC assay used for PIP was 
previously described (97). 

Chemicals and Reagents 

Piperacillin, p-aminobenzoic acid polyester were purchased from Sigma Chemical 
Company (St. Louis, MO), and used as received. Tazobactam was donated by Lederle 
(Divisional Laboratory, Cyanamid of Great Britain, Hampshire, England). Antipyrine was 
purchased from Aldrich Chemical Company (Milwaukee, WI). HPLC grade acetonitrile 
and tetrabutylammonium hydroxide (TBA) were purchased from Fisher Scientific (Fair 



39 



40 



Lawn, NJ). All other reagents were of analytical grade and purchased from Fisher 
Scientific. 

Instrumentation 

The chromatographic system consisted of a Constametric III G high pressure 
pump (LDC Milton Roy, Riviera Beach, FL), a Perkin Elmer auto sampler (model ISS- 
100, Norwalk, CT), fitted with a 100 |iL injection loop, a 15 cm x 4.6. mm i.d., 5 |im 
particle size Spherisorb Cjg column (PhaseSep, Quensferry, UK), a UV LDC Milton Roy 
detector (Riviera Beach, FL), and a Hewlett Packard integrator (model 3392A, Palo Alto, 
CA). A pre-column filled with ODS packing material was placed before the analytical 
column. 

TZB Sample Preparation 

To 100 [iL of rat plasma 500 of ice cold acetonitrile with 1% of formic acid 0.5 
M and 50 |iL of antipyrine 2 mg/mL (internal standard) were added. This step was 
performed in an ice bath. The mixture was vortexed for 10 seconds and then centriftiged 
at 3000 rpm for 20 min. The supernatant was evaporated to dryness under nitrogen. The 
residue was reconstituted in 200 |iL of water and 100 |iL were injected into the HPLC 
system. Tissue samples obtained by microdialysis were injected directly using a manual 
injector with a 20 \xL loop. 

TZB Chromatographic Conditions 

TZB was analyzed using an ion pair reversed phase HPLC system. The mobile 
phase consisted of a mixture of 5 mM TBA, 0.04 M sodium phosphate monobasic 
solution and acetonitrile (46.5:46.5:7 % V:V). The pH was adjusted to 6.6. The mobile 
phase was filtered through a 0.2 mm nylon filter and degassed by sonication before use. 



41 



The flow rate was 1 mL/min and the wave length used for detection was 220 nm. Typical 
blank plasma and TZB chromatograms obtained after extraction are shown in Figure 3- la. 

PIP Sample Preparation 

To 100 |iL of rat plasma 200 [iL of methanol containing 15 |ig/mL of p- 
aminobenzoic acid propylester (internal standard) were added. The mixture was vortexed 
for 15 seconds and subsequently centrifliged at 3000 rpm for 15 min. An aliquot of 100 
[iL of the supernatant was injected into the HPLC system. Tissue samples from 
microdialysis were injected directly using a manual injector with a 20 ^iL loop. 

PP Chromatographic Conditions 

For PIP analysis, reversed phase chromatography was performed. The mobile 
phase consisted of 0.05 M phosphate buffer and acetonitrile (80:20 % V: V). The pH was 
adjusted to 7. The mobile phase was filtered and degassed as described for TZB mobile 
phase. The flow rate was 1 mL/min and the UV detection was also performed at 220 nm. 
Figure 3- lb. shows a typical PIP chromatogram after extraction and the respective blank 
plasma chromatogram. 

Assay Validation 

Both assays described above were validated in plasma by preparing three 
calibration curves each day for three different days and analyzing quality control samples. 
For TZB a linear calibration curve could be obtained for peak height ratio in the range of 3 
to 200 ng/mL. For PIP a linear calibration curve could be obtained for peak area ratio in 
the range of 2 to 500 ng/mL. In both cases the correlation coefficients obtained were 
0.996 or more. Inter- and intraday variability were determined by using four different 



42 



quality control concentrations for TZB (3, 30, 75 and 150 |ag/mL) and three for PIP (30, 
100 and 300 \xg/mL). 



Figure 3-1. Representative chromatograms of tazobactam and piperacillin in rat plasma: a) 



shows blank plasma and tazobactam (RT 6.54 min) with internal standard (RT 
11.70 min); b) shows blank plasma and piperacillin (RT 6.09 min) with 
internal standard (RT 13.04 min). 



TZB Stability Studies 

The stability of TZB was determined in different media and conditions. Wistar rat 
plasma was spiked with TZB to obtain a final concentration of 100 )ig/mL and kept at 
room temperature or at 37 ° C up to three hours. Aliquots (100 |.iL) were taken at time 
zero, 15, 30, 60, 90, 120 and 180 min and immediately analyzed using the analytical 
method described above. The stability of TZB in rat plasma filtrate was investigated at 
room temperature. Rat plasma filtrate was obtained by ultracentrifijgation of untreated 



« 




a 



b 



43 



plasma using an ultra-microcentriflige tube filter unit (PGC Scientifics, Gaiterburg, MD) 
with a molecular weight cut off of 5000 D. Centrifligation was performed in an 
ultracentrifuge (Marathon 13K/M, Fisher, Fair Lawn, NJ) at 4500 rpm for 20 min. The 
rat plasma filtrate was spiked with TZB to obtain a final concentration of 100 |ig/mL. 
Samples (100 |iL) were taken at time zero, 5, 10, 15, 30 and 60 min. The filtrate was 
analyzed using the same method described for blood samples. All the experiments for the 
stability studies were replicated three times. 

TZB stability was also determined in water, phosphate buffer 0.05 M pH 7 and 
Muller-Hinton Broth solution (MHB). Solutions containing TZB at final concentrations 
of 100 i^g/mL were prepared in water and phosphate buffer and kept at 4 ° C for 72 h. 
Samples (100 |iL) were taken at time zero, 1, 2, 3, 24, 48 and 72 h and analyzed by 
HPLC. The stability of TZB in MHB was checked at 37 ° C in presence or absence of 
Escherichia coli ATCC 25922 (piperacillin sensitive, p-lactamase negative). TZB was 
dissolved in MHB to obtain a solution with a final concentration of 100 |ig/mL. In the 
media containing E. coli the bacteria was added to produce an inoculum of 5 x 10^ 
bacteria/mL. From this solution aliquots (100 |iL) were taken at time zero, 1, 2, 3, 4, 5, 6, 
7, 8, and 24 h. The samples were extracted in the same way as blood samples and 
analyzed by HPLC using a calibration curve prepared in broth solution. 

Results and Discussion 

Assav Validation 

The results of the inter- and intraday variability in plasma for tazobactam and 
piperacillin are shown in Tables 3-1 and 3-2, respectively. 

Based on the results of the validation, both assays were considered adequate for 
the purpose of this study. The limit of quantification (LOQ) for piperacillin and 



44 



Table 3-1. Inter- and intraday variability for tazobactam assay (n = 9). 



Theoretical 
Concentration 
(Hg/mL) 


Measured 
Concentration (SD) 
(|ig/mL) 


Intraday Variability 
(%) 


Interday Variability 
(%) 


3 


3.8 (0.72) 


10.0 


18.7 


30 


31.4(2.8) 


4.4 


8.9 


75 


72.2 (2.0) 


5.5 


2.8 


150 


152.8(15.8) 


3.9 


10.3 



Table 3-2. Inter- and intraday variability for piperacillin assay (n = 9). 



Theoretical 
Concentration 
(Hg/mL) 


Measured 
Concentration (SD) 
(l-ig/mL) 


Intraday Variability 
(%) 


Interday Variability 
(%) 


30 


28.9(1.9) 


2.7 


6.6 


100 


96.0 (4.3) 


3.6 


4.5 


300 


296 (4.2) 


1.6 


4.2 



tazobactam in plasma, determined as the lowest concentration that produced an interday 
variability smaller than 20%, were 2 \ig/mL and 3 ng/mL, respectively. For the 
microdialysis studies the LOQ was 1 ng/mL for both drugs. 

TZB Stabilitv Studies 

The results of the stability studies of TZB in rat plasma and rat plasma filtrate are 
shown in Figure 3-2. The half-lives of TZB in rat plasma at room temperature and at 
37 ° C were estimated to be 62 (± 9) min and 34 (± 2) min, respectively. In rat plasma 
filtrate at room temperature the half-life was 84 (± 10) min. 

The concentrations of TZB in water and phosphate buffer after 72 h at 4 ° C 
dropped by an average of 12% and 6%, respectively. In broth solution, 85% of the initial 



45 



concentration is available after 24 h at 37 ° C. The presence of £. coli ATCC 25922 did 
not change the rate of TZB degradation under these conditions. 

Based on these results and literature data on the instability of TZB in plasma kept 
at -20 ° C (164) it was concluded that plasma samples from the pharmacokinetic studies 
should be extracted immediately after they are obtained. It was also shown that the 
determination of protein binding by ultrafiltration is problematic since TZB is not stable in 
plasma and in plasma filtrate. 

Conclusions 

It can be concluded that the HPLC assays for piperacillin and tazobactam are 
precise and accurate. 

Tazobactam rapidly degrades in plasma at room temperature and 37 ° C as well as 
in plasma uhrafiltrate. Hence, the determination of TZB protein binding by uhrafiltration 
does not seem feasible. Tazobactam is stable in Miiller-Hinton Broth solution in the 
conditions that will be used for the pharmacodynamic studies, in the absence and presence 
of non p-lactamase producer £. coli. 



46 




10° I I 

10 20 30 40 50 60 

Time (min) 

Figure 3-2. Stability of tazobactam: a) in rat plasma at room temperature (half-life 62 ± 9 
min); b) in rat plasma at 37 ° C (half-life 34 + 2 min); c) in rat plasma filtrate 
at room temperature (half-life 84 + 10 min). Mean + SD of 3 experiments. 



CHAPTER 4 

PHARMACOKINETICS OF PIPERACILLIN AND TAZOBACTAM 

COMBINATIONS 



Specific Aims of the Pharmacokinetic Studies 

The specific aims of the pharmacokinetic studies were: to elucidate the 
pharmacokinetics of tazobactam in rats using plasma data and free interstitial 
concentrations obtained by microdialysis, to determine the pharmacokinetics of 
tazobactam combined with piperacillin when administered to rats in different dose 
combinations (1:4 and 1:8) using plasma and free interstitial concentrations obtained by 
microdialysis, to validate the hypothesis that the concentration-time profile of piperacillin 
in plasma and tissue is not affected by the administration of tazobactam. Dose ratios of 
tazobactam-piperacillin 1:2 and 1:4 will be investigated. Furthermore, the 
pharmacokinetic studies inteds to show that diffusion is the mechanism that drives the 
distribution of tazobactam between blood and tissues when administered alone or in 
combination with piperacillin, to correlate free levels of the combination tazobactam and 
piperacillin in blood with those in tissue obtained by microdialysis, and to predict tissue 
concentrations of both drugs alone and in combination based on plasma data. 

Material and Methods 

Experimental Design 

Tazobactam and piperacillin are administered to humans in two dose ratios: 1 :4 
and 1 : 8. In a previous study wich investigated the pharmacokinetics of piperacillin alone 



47 



48 



in rats, two different doses were used: 60 and 120 mg/kg (97). The dose ratios studied in 
this project are based on the same doses of piperacillin in order to allow for comparisons. 

Male Wistar rats weighing 270-3 10 g were divided into 7 groups with 6 animals 
per group. The pharmacokinetics of tazobactam alone was studied for three different 
doses: 15 mg/kg, 30 mg/kg or 60 mg/kg body weight. For the determination of 
piperacillin's influence on tazobactam pharmacokinetics, three combinations were studied: 
TZB 15 mg/kg and PIP 60 mg/kg (1 :4) or PIP 120 mg/kg body weight (1:8), and TZB 30 
mg/kg and PIP 120 mg/kg body weight (1 :4). The influence of tazobactam on piperacillin 
pharmacokinetics was determined for two combinations: TZB 15 mg/kg or 30 mg/kg and 
PIP 60 mg/kg body weight (1 :4 or 1 :2). Although the TZB-PIP dose ratio 1 :2 is not used 
for treatment of infections, it was investigated in this project to determine if higher doses 
of tazobactam would have an effect on piperacillin pharmacokinetics. In all studies the 
drugs were administered as an i.v. bolus injection. 

Surgical Procedure 

The animal procedure was approved by the Institutional Animal Care and Use 
Committee of the University of Florida (lACUC). Rats were anesthetized with 
ethylcarbamate (1 .25 mg/kg i.p.). After complete anesthesia the animals were immobilized 
in a supine position and a catheter was inserted into the carotid artery (polyethylene 
catheter with an inner diameter of 0.3 mm and an outer diameter of 0.7 mm). The artery 
was irrigated with heparinized saline. The left hind leg muscle was used for the insertion 
of the microdialysis probe after skin removal. The microdialysis probe was allowed to 
equilibrate inside the muscle for one hour before drug administration. Drugs were injected 
as i.v. bolus injection (0.5 mL/100 g) via the femoral vein of the right hind leg. After the 
completion of the injection (time zero), blood and microdialysis tissue samples were 
drawn. Microdialysis samples were collected over 20 min intervals. Blood samples were 



49 



collected right before drug administration and at 2, 5, 10, 15, 20, 30, 45, 60, 90, and 120 
minutes. Blood samples (400-500 |iL) were harvested into heparinized tubes. Plasma 
samples for TZB analysis were immediately extracted as described in analytical 
methodology. Plasma samples for PIP analysis were frozen and stored at -5 ° C until 
assayed. 

Microdialvsis Conditions 

Microdialysis was used to determine free tissue concentrations of the drugs under 
investigation. A single microdialysis probe was inserted into the left leg muscle of the rat 
when TZB was administered alone. For the investigation of tissue concentrations after 
administration of the combination of TZB and PIP two probes were inserted in the same 
muscle. Each probe was previously calibrated in vitro for either PIP or TZB. The 
microdialysis pump was set at a flow rate of 1.5 |al/min. Ringer's solution was used as 
perfiision fluid. Dialysate samples were collected over 20 min time intervals and 
immediately analyzed by HPLC. Since microdialysate concentrations are time-averaged 
over the collection interval these values were translated into concentration at a single time 
point by assuming that the concentration obtained is the actual concentration at the midle- 
point of the time interval. 

Microdialvsis Svstem and Probe Calibration In Vitro 

The microdialysis system consisted of a Harvard Apparatus Pump 22 connected to 
a microliter syringe (1 mL, gas-tight) to provide the perfiisate solution. The syringe was 
connected to the flexible loop probe (tip length 4 mm, molecular weight cut off 6000 D) 
(ESA, Inc., Bedford, MA) by using fused-silica connecting tubes. The lag time due to the 
dead volume between the sampling site and the point of dialysate collection was calculated 



50 



to be 27 sec. The lag time was considered negligible and no corrections were made in the 
time-points. 

Prior to each in vivo experiment the microdialysis probes were calibrated in vitro. 
The recovery obtained was used to normalize the in vivo data. The probes were put into 
Ringer's solution containing either TZB or PIP 100 |ig/mL and allowed to equilibrate for 
one hour at 37 ° C. Ringer's solution was perfused at 1.5 |iL/min. After the equilibration 
period 3 samples were collected at 20 min intervals and analyzed by HPLC. The recovery 
was determined as the ratio of dialysate concentration over outside concentration x 100. 
Under these conditions the recoveries of TZB and PIP were found to be in the range of 
18-32% and 8-14%, respectively. 

TZB Protein Binding Determination 

The determination of protein binding by ultrafiltration was not feasible since it was 
shown that TZB degradation is rapid in rat plasma and rat plasma ultrafiltrate. The 
protein binding was determined as the ratio between free tissue concentration and total 
plasma concentration obtained at steady state following a constant intravenous infusion. 
At steady state the free concentrations of the drug in tissue and plasma are in equilibrium 
and the ratio between free concentration in tissue and total concentration in plasma can be 
used to assess the fraction bound to plasma proteins. 

For the infusion experiments a loading dose followed by a maintenance dose of 
TZB alone were given in order to reach a steady state concentration in plasma of 50 
Hg/mL. Seventy five minutes after the TZB loading dose, piperacillin was also 
administered to the same animal in order to determine the influence on this drug on the 
protein binding of TZB. Piperacillin was administered as a loading dose followed by a 
maintenance dose to reach a steady state concentration in plasma of 200 |ig/mL (1:4 TZB- 
PIP ratio). The maintenance doses were given in form of a constant intravenous infiision 



51 



in the femoral vein. A flow rate of 2 mL/h was maintained using a volumetric infiision 
pump Flo-Gard 8000 (Travenol Laboratories, Deerfield, EL). Microdialysis was 
performed as described for the single dose administration. One hour of probe 
equilibration in the muscle was allowed before drug administration. Microdialysis samples 
were collected over 20 min intervals. Blood samples were collected before dosing and at 
15, 30, 45, 60, 75 min to analyze TZB levels administered alone and at 85, 100, 120, 140, 
180, 210, and 240 min for analysis of TZB administered in combination. A total of 3 
animals were used for the infusion studies. 

The loading and maintenance doses were calculated based on pharmacokinetic 
parameters estimated from single intravenous dose administration of TZB or PIP using the 
following equations: 

LD = VcCp^^ (4-1) 



where Vc is the volume of distribution of the central compartment and Cpgs is the target 
concentration in plasma. The infusion rate was calculated using eq. 4-2: 

Ko = CpssCL (4_2) 

where CL is the total clearance. 

Microdialysis Probe Calibration In Vivo 

The in vivo recovery of the microdialysis probe for tazobactam was determined by 
using the point of no net flux method. For one group of three animals, a loading dose 
followed by a maintenance dose of TZB alone were administered to obtain a steady state 
concentration of 50 ^g/mL. The same infusion conditions described for protein binding 
determination were followed. One hour afler the LD was administered (steady state 



52 



condition established), three microdialysis samples were collected using plain Ringer's 
solution as perfusate. For the subsequent samples, TZB was added in different 
concentrations (7.5, 15 or 30 ng/mL) to the perfusion fluid. After one hour equilibration 
with the new perfusate concentration, the net dialysate concentration was determined for 
three samples by HPLC. The net concentration in the dialysate solution was plotted 
against the initial perfusate concentration. The intercept of the plot with the x-axis equals 
the free concentration of TZB in the tissue at steady state. The slope of the line is the in 
vivo recovery. The same probe was calibrated in vitro, prior to the experiment, and in 
vivo using the conditions describe above. A correction factor was calculated and used to 
normalize all TZB microdialysis data before estimation of pharmacokinetic parameters. 
No correction factor was used for piperacillin since it was shown that the in vitro and in 
vivo recoveries were similar in the experimental conditions described (97). 

Estimation of Pharmacokinetic Parameters 

The pharmacokinetic parameters of TZB alone and in combination as well as the 
parameters of PIP in combination were estimated for each animal using classical non- 
compartmental equations (165). The terminal elimination rate constant (kg) was estimated 
from the log-linear plot of concentration versus time. The area under the concentration- 
time curve (AUC) and the area under the first moment curve (AUMC) were calculated 
using the trapezoidal rule. The following parameters were also determined: mean 
residence time (MRT), the half-life (ti/2), the volumes of distribution (Vc, Ydgg and 
Vdarea) and the total clearance (CL). 

The compartmental analysis was performed using the computer program 
SCffiNTIST (Micromath, Salt Lake City, UT). The average data for both drugs alone 
and in combination were fitted using a two compartment body model according to eq. 4-3: 



53 



Cp = Ae 



(4-3) 



where Cp is the total plasma concentration at time t, a and 3 are the hybrid constants for 
the distribution and elimination phases, respectively, and A and B are the corresponding 
zero-time intercepts. All data points were weighted equally for the compartmental fitting. 

The concentrations of free piperacillin and tazobactam in the peripheral 
compartment were predicted based on plasma pharmacokinetic parameters obtained from 
the plasma data using the following equation (166): 

Sissue-vc.(a-p) r 'J 

where ^li^ = A-3 + Ba (4-5) 
Vc 



where fii is the fraction unbound of the drug in plasma, D is the dose administered as i.v. 
bolus injection, k2\ is the first-order rate constant from the peripheral to the central 
compartment. 

Statistical Analysis 

The values of pharmacokinetic parameters obtained from the non-compartmental 
approach were compared using analysis of variance (ANOVA). When significant 
differences were observed Duncan's multiple range test was applied for individual 
comparisons. For the compartmental analysis the model selection criteria (MSG) was 
used to determine the goodness of the curve fit. 



54 



Results and Discussion 



Piperacillin Pharmacoldnetics 

Since the i?j vitro and in vivo recoveries for PIP were similar (8 to 14%), no 
correction factor was used to normlize PIP microdialysis data. The results of the non- 
compartmental analysis of PIP 60 mg/kg in plasma and in tissue, alone (97) and in 



Table 4-1. Pharmacokinetic parameters of piperacillin 60 mg/kg alone and in combination 
with tazobactam 30 mg/kg (1:2) (n = 6), tazobactam 15 mg/kg (1:4) (n = 6), 
and average of both combinations pooled (n = 12). (Mean ± SD). 



Pharmacokinetic 
Parameters 


Piperacillm 
Alone ^ 


PIP/TZB 
(1:2) 


PIP/TZB 
(1:4) 


PIP/TZB 
Average 


AUC Plasma 
(|ig.min/mL) 


4662 ± 1899 


4863 ± 2244 


41 10 ±2020 


4342 ± 2027 


MRT Plasma 
(min) 


32 ± 8 


42 ±25 


38±21 


39±21 


Half-life Plasma 
(min) 


33 ±6 


42± 16 


38± 15 


39± 15 


Vc 
(L/kg) 


0.17±0.03b 


0.22 ± 0.02 


0.26 ±0.06^ 


0.25 ± 0.06b 


Vdss 
(L/kg) 


0.33 ± 0.20 


0.49 ±0.12 


0.56 ±0.14 


0.54 ±0.13 


Vdarea 
(L/kg) 


0.51 ±0.34 


0.81 ±0.34 


0.84 ±0.23 


0.83 ±0.25 


CL 

(mL/min/kg) 


11.7±8.3 


14.8 ±7.2 


17.9 ± 8.2 


16.9 ±7.7 


AUC Tissue 
(lag. min/ mL) 


2533 ± 942 


2515 ± 817 


3562 ± 1474 


3143 ± 1327 


MRT Tissue 
(min) 


35±11 


39± 16 


46 ± 14 


43 ± 14 


Half-life Tissue 
(min) 


30 ±7 


27 ±9 


31 ± 10 


29 ±9 



a From Nolting et al. (1996) (97); b p<0.05. 



55 



combination with TZB 15 and 30 mg/kg (1 :4 and 1 :2 ratios) are summarized in Table 4-1. 
There were no statistically significant differences between the non-compartmental 
parameters estimated for PIP in either combination (1 :2 and 1 A), leading to the 
conclusion that if TZB has an affect of PIP pharmacokinetics this effect is not dose 
dependent. For this reason, the concentration-time profiles for these two ratios were 
pooled together and the average of the pharmacokinetic parameters were estimated for 
PIP combined. The results are also shown in Table 4-1 . When PIP alone was compared 
to PIP in combination no significant difference was observed, showing that the 
administration of TZB does not affect PIP pharmacokinetics. The volume of distribution 
in the central compartment (Vc) was the only parameter that showed significant difference 
when PIP alone was compared to PIP (1 :4) or PIP combined average. 

Concentration time profiles of free PIP in plasma and tissue after administration of 
60 mg/kg in combination with TZB are shown in Fig. 4-1 . The values shown represent 
the average of all 12 animals from the two groups (1 :2 and 1 :4). As can be seen in Figure 
4-1 the free plasma concentration-time profile of PIP could be fitted to a two- 
compartment body model like it was earlier shown for PIP alone (97). The MSG for this 
fit was higher than 6. Free concentrations in tissue were predicted by using eq. 4-4 and 
are also shown in Fig. 4-1 together with the free interstitial levels measured by 
microdialysis. The hybrid constants used for these predictions were obtained fi-om the 
plasma fitting: A = 261.5 ± 6.3 ng/mL, B = 59.3 + 5.4 ng/mL, a = 0.236 + 0.134 min"!, 
and P = 0.025 ± 0.003 min'!. The value used for fraction unbound of PIP (fu = 0.55) was 
determined previously for PIP alone (97). It can be seen that the predicted line is in good 
agreement with the measured free interstitial concentrations proving that diflaision is the 
process that governs the transfer of fi-ee Pff between blood and tissue. After a short 
distribution phase, the concentrations in tissue and plasma are in equilibrium. The 
concentration in the peripheral compartment is higher than the concentration in the central 
compartment due to elimination from the central compartment only. As expected from a 



56 



diffusion driven process the slopes of the terminal phases are statistically similar showing 
that the disappearance of the drug from both compartments occurs at similar rates. 



103 




10'' ~f ' ' I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r 



20 40 60 80 100 120 

Time (min) 

Figure 4-1. Concentration-time profiles for free piperacillin levels in plasma (•) and 
interstitial fluid (O) after administration of 60 mg/kg i.v. bolus combined 
with tazobactam in two different ratios (1 :2 and 1 :4). Plasma concentrations 
were fitted to a two-compartment body model. The line for fi-ee tissue levels 
represents the prediction based on plasma data. Points represent mean ± SD 
of 12 animals. 



TZB Probe Calibration In Vivo 



The results of the in vivo calibration for TZB according to the point of no net flux 
are shown in Figure 4-2 for a representative experiment. In this example, the in vitro 



57 



recovery determined prior to the experiment with this probe was 24%. The point of no 
net flux which equals the free interstitial concentration was calculated as 9 ^g/mL. The in 
vivo recovery calculated based on the slope of the regression line was found to be 23%. 
For the other two experiments, the in vitro recoveries were determined to be 30% and 
32%, with the respective in vivo recoveries of 24% and 27%. The correction factor was 
calculated to be in average 1.16. This factor was used to normalize the microdialysis data 
for TZB administered alone or in combination with PIP. 




Coricentration (ng'mL) 



Figure 4-2. Tazobactam in vivo calibration using point of no net flux method in a single 
rat. Plot of initial perfusion fluid concentrations of TZB versus net changes in 
the dialysate concentrations. Intercept at 9 |ig/mL represents free interstitial 
concentration. In vivo recovery of 23% calculated from the slope. 



58 



Protein Binding Determination 

Tazobactam protein binding was calculated as the ratio between free interstitial 
concentration and total plasma concentration obtained after intravenous constant infusion. 
The average levels in plasma and tissue obtained after three experiments are shown in 
Figure 4-3 . The free interstitial levels were normalized for the in vivo probe calibration. 
Under these conditions the fraction unbound was determined to be 0.32 ± 0.03 for TZB 
administered alone and 0.26 ± 0.04 for TZB in combination with PIP. Since no significant 
statistical difference was observed, the overall fraction unbound was calculated as 0.28 ± 
0.05. 

103 ^ 




IQO ""j I I I I I 1 — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — I — 
50 100 150 200 250 

Time (min) 

Figure 4-3. Tazobactam total plasma concentrations (■) and free interstitial 
concentrations (□) at steady state following a constant i.v. infusion. TZB 
administered alone followed by LD of piperacillin and maintenance doses 
of TZB and PIP (1:4) at 75 min. Points represent mean ± SD of 3 animals. 



59 



The average total plasma concentration of TZB alone under the infusion conditions 
described above was 35 ± 2 ng/mL. Assuming this total plasma concentration and the 
fraction unbound determined, one can expect a free interstitial concentration of TZB to be 
in the range of 9.2 to 10.4 ng/mL. The free concentration determined during the in vivo 
calibration (9 ^g/mL) is very close to this range, considering that those two concentrations 
were determined in different animals. This fact fiarther validates the protein binding value 
for TZB determined in this study. 

Tazobactam Pharmacokinetics 

Tazobactam alone 

Tazobactam alone was administered in three different doses: 15, 30 and 60 mg/kg. 
Total plasma concentration-time profiles of these three doses are shown in Figure 4-4. As 
can be seen from the plot a two-compartment body model sufficiently describes the data in 
all three cases. Results of the compartmental analysis performed with the average data are 
shown in Table 4-2. The MSC and the correlation coefficients obtained for these fittings 
confirm the choice of the two-compartment model. 

Resuhs of the non-compartmental analysis of the plasma and tissue data are 
summarized in Table 4-3. Linear pharmacokinetics can be observed for the two lowest 
doses: 15 and 30 mg/kg. As expected, the AUC doubled when the dose was increased 
from 15 to 30 mg/kg. A trend of decreasing clearance with increasing concentration was 
observed, but the differences did not prove to be significant, probably due to the high 
variability observed in these experiments. All the other parameters estimated were not 
statistically different. 

Non-linear pharmacokinetics was observed between the 30 and 60 mg/kg doses. 
The AUC increased more than three times between these two doses and was statistically 
significant. The average half-life and MKT also increased although the differences were 



60 



not statistically significant. The increase in half-life for the highest dose can also be 
observed in Figure 4-4. 

103 T 




Time (min) 

Figure 4-4. Total plasma concentration-time profile of tazobactam alone: 15 mg/kg (■), 
30 mg/kg (•) and 60 mg/kg(A). Points represent mean ± SD of 6 animals. 

The same differences showed for the plasma pharmacokinetics were also observed 
for the tissue data. No data is reported in tissue for TZB 15 mg/kg because the levels 
were very close to the limit of quantification of the analytical method. The results of the 
non-compartmental analysis in tissue for the two highest doses are shown in Table 4-3. 
The AUC tissue increased more than three times from 30 to 60 mg/kg following the 
results observed in plasma. The MRT and the half-life in tissue showed a significant 



61 



Table 4-2. Pharmacokinetic parameters obtained by compartmental analysis of the average 
concentration-time profiles of TZB alone or in combination with PIP. (Mean + 
SD). 



Drug 
Combination 
(mg/kg) 


A 

(^g/mL) 


i> 

(Mg/mL) 


a 

(min') 


P 

(min') 




MSC 


TZB alone 15 


48.2 
(0.8) 


15.8 
(0.3) 


0.35 
(0.01) 


0.022 
(0.001) 


0.99 


8.0 


TZB alone 30 


82.2 
(1.8) 


44.7 
(1.1) 


0.29 
(0.01) 


0.026 
(0.001) 


0.99 


1.1 


TZB alone 60 


176.0 
(12.5) 


63.8 
(3.9) 


0.22 
(0.02) 


0.011 
(0.001) 


0.99 


3.4 


TZB 15/PIP 60 
(1:4) 


59.1 
(2.6) 


30.0 
(2.2) 


0.22 
(0.02) 


0.020 
(0.002) 


0.99 


5.7 


TZB 15/PIP 120 
(1:8) 


75.2 
(9.8) 


35.9 
(2.2) 


0.30 
(0.05) 


0.018 
(0.001) 


0.99 


4.8 


TZB 30/PIP 120 
(1:4) 


108.9 
(11.4) 


65.6 
(6.3) 


0.28 
(0.06) 


0.024 
(0.003) 


0.99 


4.4 



increase confirming the trend observed for the plasma data. As expected, the MRT and 
the half-life did not differ significantly between plasma and tissue for each dose analyzed 
individually. Since the AUC increased proportionally in plasma and tissue, the fraction 
unbound determined by the ratio between AUC tissue and AUC plasma was similar for 
both doses. These values are in good agreement with the TZB protein binding determined 
previously in the infusion experiments. According to the results presented, one can infer 
that the observed TZB non-linearity between these two doses (30 and 60 mg/kg) is not 
related to saturation of protein binding sites. 

The predicted free tissue concentrations of TZB 30 mg/kg and 60 mg/kg 



62 



Table 4-3. Pharmacokinetic parameters of tazobactam alone determined by non- 
compartmental analysis. (Mean ± SD). 



Pharmacokinetic 
r aranieiers 


TZB 15 mg/kg 


TZB 30 mg/kg 


TZB 60 mg/kg 


Auu riasma 
(|ig.min/mL) 


1179 + 688'^ 


2621 ± 1133'' 


8538 ± 3863^ 


JVLKl riasma 
(min) 


76 ± 52 


53 ± 32 


119 ± 70 


riaii-iite riasma 
(min) 


51 ± 32 


43 ± 24 


90 ± 51 


VC 

a/kg) 


0.41 ± 0.12 


0.33 ±0.11 


0.31 +0.03 


VOss 

(L/kg) 


0.91 ± 0.27 


0.61 ± 0.29 


0.80 ± 0.21 


Vdarea 
(L/kg) 


0.94 + 0.23 


0.72 ± 0.35 


0.88 ± 0.22 


(mL/min/kg) 


19.1 ± 14.2 


13.5 ± 5.8 


8.3 ± 3.8 


ATIC Tissue 
(Hg.min/ mL) 


nd 




OCiA^ 4- 4773 
/U'+ J X 4 / /" 


MRT Tissue 
(min) 


nd 


54±2ia 


95 + 35a 


Half-life Tissue 
(min) 


nd 


40 ± 15a 


71 ± 26a 


Fraction Unbound 


nd 


0.24 + 0.10 


0.2610.06 



a p<0.05; nd = not determined 



administered alone based on total plasma data together with the free plasma 
concentrations are shown in Fig. 4-5. The predictions were calculated by using eq. 4-4 
and the hybrid constants shown in Table 4-2 obtained from plasma data. The fraction 
unbound used in each case is reported in Table 4-3. As observed for PEP, after 
equilibrium is reached between free concentrations in tissue and free concentrationsin 
plasma, the concentrations in tissue are slightly higher than that in plasma due to the 



63 





Figure 4-5. Concentration-time profiles of free tazobactam levels in plasma (filled 
symbols) and interstitial fluid (open symbols) after administration of 30 
mg/kg (circles) or 60 mg/kg (triangles) i.v. bolus. Plasma concentrations 
fitted to a two compartment body model. The line for fi-ee tissue levels 
represents the prediction based on plasma data. Points represent mean ± SD 
of 6 animals. 



64 



elimination from the central compartment. The slopes of the terminal phases are similar in 
both cases showing that diffusion is the process that drives the distribution of TZB 
between blood and tissue. It can be seen that the predictions are in good agreement with 
the measured free tissue concentrations proving that it is possible to use pharmacokinetic 
parameters estimated from total plasma data to predict free interstitial concentrations of 
TZB administered alone. 
Tazobactam combined with piperacillin 

Tazobactam 1 5mg/kg was administered combined with PIP in two different ratios: 
1 :4 and 1:8. The concentration-time profiles of plasma data for these two combinations as 
well as for the same dose administered alone are shown in Figure 4-6. The results of the 
curve fitting are presented in Table 4-2. TZB administered in combination with PIP 
showed higher plasma concentrations than when administered alone. A two compartment 
body model can be used to describe the data in all cases. The goodness of fit presented in 
Table 4-2 confirms the appropriateness of the model. 

The results of the non-compartmental analysis performed for these two 
combinations are shown in Table 4-4. The results for TZB 15 mg/kg alone are shown in 
Table 4-3. There is a trend of increasing AUC by increasing the proportion of PIP in the 
combination. The difference prove to be significant for the combination TZB-PIP 1 :8 
where the AUC doubled. A statistically significant decrease in TZB volumes of 
distribution (Vc, Vdgs and Vdaj-ga) is observed when PIP is administered in combination 
compared to TZB alone. As observed for humans, the co-administration of PIP decreased 
the clearance of TZB probably because PIP interferes with TZB tubular secretion. A 
significant decrease in clearance is observed for TZB in combination. The proportion of 
PIP in combination does not seem to affect TZB volume of distribution and clearance in a 
different fashion since between the two combinations studied no statistically significant 
difference was observed for these parameters. Once TZB volume of distribution as well as 



65 



103 ^ 




20 40 60 80 100 120 



Time (min) 

Figure 4-6. Plasma concentration-time profile of tazobactam 15 mg/kg alone (■), and 

combined with piperacillin: 60 mg/kg (1:4) (•) and 120 mg/kg (1:8) (A). 
Points represent mean ± SD of 6 animals. 

the clearance are decreased in the same order of magnitude by the administration of PIP 
the half-life is expected to remain constant. The differences in half-life did not prove to be 
significant when TZB alone was compared to TZB in combination. Similar MRTs were 
also observed for these three cases. 

A higher dose of TZB (30 mg/kg) was also administered in combination with PIP 
120 mg/g (1 :4). The results of the non-compartmental analysis of this combination are 
shown in Table 4-4. The comparison between the AUC plasma for TZB 30 mg/kg in 
combination and 30 mg/kg alone (Table 4-3) confirm the trend observed for the lower 
dose. The addition of PIP in combination increased the plasma AUC of TZB, although 



66 



the difference was not statistically significant. The same can be said for the volumes of 
distribution (Vc, Ydgg and Vdaj-ga) ^"d clearance. These parameters were decreased by 
the administration of PIP but the differences were not statistically significant. As observed 
for 15 mg/kg, administration of PIP did not affect the MRT and half-life in plasma. The 
analysis of the results in tissue lead to similar conclusions. PIP caused a statistically 
significant increase in the TZB AUC tissue, confirming the results observed in plasma. 



Table 4-4. Pharmacokinetic parameters of tazobactam in combination with piperacillin 
determined by non-compartmental analysis. 



Pharmacokinetic 
Parameters 


TZB 15/PIP 60 
(mg/kg) 
(1:4) 


TZB 15/PIP 120 
(mg/kg) 
(1:8) 


TZB 30/PIP 120 
(mg/kg) 
(1:4) 


AUC Plasma 
(Hg.min/mL) 


1965 ±591 


2679 ± 974 


3725 ± 1055 


MRT Plasma 
(min) 


49± 11 


65 ±23 


58± 17 


Half-life Plasma 
(min) 


42 + 8 


49± 16 


49± 13 


Vc 
(L/kg) 


0.21 ±0.08 


0.19 ±0.03 


0.23 ± 0.02 


Vdss 
(L/kg) 


0.40 ±0.1 5 


0.37 ±0.09 


0.47 ±0.12 


Vdarea 
(L/kg) 


0.50 ±0.20 


0.40 ±0.09 


0.59 ±0.16 


CL 

(mL/min/kg) 


8.4 ±3.1 


6.5 ±3.3 


8.5 ±2.2 


AUC Tissue 
(lig.min/ mL) 


nd 


nd 


785 ± 187 


MRT Tissue 
(min) 


nd 


nd 


46± 10 


Half-life Tissue 
(min) 


nd 


nd 


41 ± 10 


Fraction Unbound 


nd 


nd 


0.22 ±0.08 



nd = not determined 



67 



No statistically significant difference were observed for MRT and half-life in tissue when 
TZB 30 mg/kg alone and in combination 1:4 with PIP were compared. The same 
parameters are in good agreement when plasma and tissue data are compared for TZB 
combined. Since both plasma and tissue AUC increased in average 44% by the 
concomitant administration of PIP, the resulting fraction unbound estimated from these 
parameters is similar to the one calculated for TZB alone. 

Free interstitial concentrations for TZB 30 mg/kg combined wath PIP 120 mg/kg 
(1:4) were estimated based on parameters obtained from fitting plasma data to a two 
compartment model (Table 4-2) by using eq. 4-4. The results of the measured free 
concentrations in the interstitial fluid obtained by microdialysis and the predictions based 
on plasma data are shown in Figure 4-7. The fraction unbound used for this prediction is 
presented in Table 4-4. 

As observed for TZB 30 mg/kg alone, TZB in combination also follows a two 
compartment body model. The measured fi^ee tissue concentrations are in good agreement 
with the predicted values calculated based on plasma data. The rates of drug 
disappearance fi-om the central and peripheral compartments are similar and elimination 
occurs only from the central compartment. Diffusion is the process that drives distribution 
of the drug between blood and interstitial space showing that it is possible to predicted 
free interstitial fluid levels using plasma pharmacokinetics for TZB in combination with 
PIP. 

Conclusions 

The main purpose of this study was to investigate the pharmacokinetics of 
piperacillin and tazobactam in plasma and tissue when administered alone and in 
combination. Microdialysis was used to measure the free concentrations of both drugs in 



103 



68 



102 - 




Time (min) 



Figure 4-7. Concentration-time profiles of free tazobactam levels in plasma (•) and 
interstitial fluid (O) after administration of 30 mg/kg i.v. bolus combined with 
piperacillin 120 mg/kg (1:4). Plasma concentrations were fitted to a two- 
compartment body model. The line for fi-ee tissue levels represents the 
prediction based on plasma data. Points represent mean ± SD of 6 animals. 



rat muscle interstitial fluid. The determination of free concentrations in tissue is an 
important issue when dealing with antiinfective agents because only the drug unbound to 
proteins is available to interact with the microorganisms in the infection site. The results 
presented showed that microdialysis is a suitable technique for investigating fi-ee levels of 
TZB and PIP alone and in combination. The in vivo calibration of the microdialysis 
probes for each individual drug is a very important aspect that has to be considered when 
using this method. In vitro and in vivo recoveries for piperacillin were similar and no 
corrections had to be made for the free tissue data. For tazobactam, on the other hand, 



69 



recoveries in vivo were lower than recoveries in vitro and the microdialysis data had to be 
normalized by a correction factor. 

The determination of protein binding is another important aspect when studying 
antiinfective agents. Tazobactam, a P-lactamase inhibitor, is very unstable in rat plasma 
making it difficult to use standard methods for protein binding determination. It was 
shown in this study that a pharmacokinetic approach can be used to estimate the protein 
binding. At steady state following a constant intravenous infusion the ratio between free 
concentration in tissue and total concentration in plasma is similar to the fraction unbound 
of the drug. Free tissue concentrations predicted using the protein binding of TZB 
determined in this way were compatible with the free concentration in the interstitial fluid 
observed in the in vivo calibration of the microdialysis probes using the point of no net 
flux. Further proof of the TZB protein binding estimate was obtained from the ratio 
between AUC tissue and AUC total plasma. Similar results were observed in all three 
approaches. 

The pharmacokinetics of piperacillin in plasma and tissue were not influenced by 
the co-administration of tazobactam. Even in a dose ratio higher than normally 
administered to patients (1:2) piperacillin pharmacokinetic parameters were not 
significantly different from the parameters estimated for PIP alone. This behavior agrees 
with the resuhs of studies performed in humans (8). Concentration-time profiles of PIP in 
combination could be described by a two-compartment body model. The measured levels 
of free PIP in tissue could be predicted based on plasma pharmacokinetics showing that 
the distribution of this drug between blood and tissue is governed by diffusion only. 

The pharmacokinetics of tazobactam alone was investigated for three different 
doses. A two-compartment body model could be used to describe the data in all cases. A 
linear relationship between concentration and the two lower doses was observed (15 and 
30 mg/kg). There was no significant differences in the elimination half-lives from the 
central compartment for both doses. A non-linear behavior was observed between 30 and 



70 



60 mg/kg. The protein binding for all three doses was constant indicating that the non- 
linearity observed is not related to saturation of protein binding sites. The free interstitial 
concentrations measured confirmed that diflfijsion is the force that drives TZB distribution 
betv^een blood and tissue. 

The co-administration of PIP affects the pharmacokinetics of TZB in rats as it was 
expected. Higher concentrations were obtained in plasma and tissue compared to TZB 
administered alone. Piperacillin decreased the volume of distribution and clearance of 
tazobactam. One explanation for the effect in clearance could be the interference of PIP 
on the tubular secretion of TZB as it was shown previously for humans. No changes in 
protein binding were observed for the combination. Tazobactam combined with PIP could 
also be fitted to a two-compartment pharmacokinetic model and diffusion was again 
shown to be the driving force for drug distribution. 

The ultimate goal of the pharmacokinetic studies was to prove the hypothesis that 
it is possible to predict free tissue levels of PIP and TZB, alone and in combination, based 
on parameters derived from plasma data. The similarity observed between the measured 
free interstitial concentrations for both drugs alone and in combination and the predicted 
levels obtained on the basis of plasma pharmacokinetics validate this hypothesis. The 
same concept observed in rats should also be applicable to humans. In this way, 
concentration-time profiles of free PIP and TZB in different combinations can be predicted 
based on humans plasma pharmacokinetics and simulated against microorganism in an in 
vitro model of infection in order to evaluate their pharmacodynamic effect. 



CHAPTER 5 

IN VITRO PHARMACODYNAMICS OF PIPERACILLIN AND TAZOBACTAM 

COMBINATIONS 

Specific Aims of the Pharmacodynamic Studies 

The specific aims of the pharmacodynamic studies were to investigate the effect of 
tazobactam on Escherichia coli in vitro, to investigate the effect of combinations of 
piperacillin and tazobactam (dose ratios 1:4, 1:8, and 1:16) on J^. coli using in vitro 
simulations of free concentration-time profiles obtained in humans after intravenous 
infusion and intravenous multiple dosing, and to test the hypothesis that tazobactam 
affects the pharmacodynamics of piperacillin against resistant bacteria. 

Material and Methods 

Drugs 

Piperacillin and tazobactam stock solutions were freshly prepared in destilled water 
for all experiments. The solutions were filtered through 0.2 ^m sterile filters (Sterile 
Accords, Gelman Sciences, Ann Arbor, MI) before their utilization in all experiments. 

Bacteria 

Escherichia coli ATCC 35218 was used as test strain in all experiments. This 
strain is resistant to PIP alone due to the production of (3-lactamases. The resistance is 
mainly due to plasmid encoded (TEM-1) although the production of a chromosomal P- 
lactamase has been reported (167). For this reason this bacteria is only susceptible to the 



71 



72 



combination of PIP and TZB. The MIC for PIP alone against E. coli ATCC 35218 was 
reported to be 32 |ig/mL or larger and the MIC for the combination, 1-2 jig/mL (167- 
168). 

The MIC for PIP was determined by broth dilution method according to standard 
procedure using Muller-Hinton Broth solution (MHB) (33). The MHB was supplemented 
with Mg2+ (25 ng/mL) and Ca2+ (50 ng/mL). The concentration of TZB (0.5 ng/mL) 
was kept constant in all dilution tubes. The inoculum contained 5 x 10^ colony forming 
units per milliliter (CFU/mL). In these conditions the MIC for PIP was found to be 1-2 
^g/mL which agrees with the literature values reported. 

In Vitro Model of Infection 

A one-compartment in vitro model of infection was used to simulate the free 
concentrations of PIP and TZB expected in human tissue based on plasma 
pharmacokinetic data. Bacteria were exposed to different combinations of these two 
drugs simulating constant concentrations, expected after constant intravenous infusion, as 
well as fluctuating concentrations obtained after multiple dose i.v. bolus administrations. 

The in vitro infection model consisted of a 40 mL culture flask filled with 20 mL of 
supplemented MHB. A syringe connected to a sterile 0.2 ^m filter was adapted to the 
upper side of the flask to allow the withdrawl and replacement of broth solution to the 
model when simulating fluctuating concentrations. The inoculum was not affected by the 
withdrawl of broth solution since this filter does not allow the passage of bacteria. In 
order to reproduce the one hour half-life of Pff-TZB in humans a stepwise dilution 
procedure was followed. At 15 min intervals, 3.2 mL of the in vitro media were 
withdrawn fi-om the system and replaced by fi-esh plain broth solution. The concentration 
of the drugs was kept constant during each of these 15 min intervals. The in vitro model 



73 



was kept at 37 ° C during the experiment. The broth solution used for the dilutions was 
also maintained at the same temperature. 

The inoculum was prepared from colonies incubated overnight on agar blood 
plates. The colonies were diluted in 0.9% saline. The turbidity of the suspension obtained 
was compared to the McFariand Equivalence Turbidity Standard (Remel Microbiology 
Products, Lenexa, KS) in order to obtain a suspension of 1 x 10^ CFU/mL. An aliquot of 
this suspension (10 ^1) was added to the in vitro model to produce a final inoculum of 
approximately 5 x 10^ CFU/mL. The model was incubated for 2 h to allow the bacteria to 
reach the log-growth phase before the addition of any drug. 

Bacterial Quantification 

Samples (50 ^L) were collected from the in vitro model and bacterial counts were 
determined by plating three serial 10-fold dilutions of the sample on blood agar plates 
(Blood Agar Plates TSA vidth 5% sheep blood, Remel, Microbiology Products, Lenexa, 
KS). The dilutions were made in 0.9% saline. Aliquots (100 \xL) of each dilution were 
plated in duplicate. The plates were incubated at 37 ° C for 18 to 24 h before reading. The 
average coefficient of variation for replicates done on different days was approximately 
40%. This variability is acceptable since the range of measured CFU values covered up to 
six orders of magnitude. 

Comparison Between Human Tissue Levels and In Vitro Levels 

In order to assure that the dilution method used to simulate the half-lives of PIP 
and TZB in human tissue was able to reproduce the desired levels, PIP and TZB 
concentrations were determined by HPLC in some experiments. Levels of PIP in the in 
vitro model were measured for eight hours using a starting concentration of 100 pg/mL 
combined with TZB 16 ^ig/mL. The experiment followed the same conditions presented 



74 



above without the presence of the bacteria. The half-life simulated was one hour. TZB 
concentrations could not be measured in this experiment because its LOQ in broth solution 
was very high (10 ^ig/ml). TZB and PIP levels were determined in the in vitro model 
using phosphate buffer 5 mM instead of MHB solution as media. The initial 
concentrations were the same specified above. Two dosing intervals of four hours were 
simulated. Three experiments were conducted in each case. 

Piperacillin Stability In The In Vitro Model 

The stability of piperacillin alone was investigated in the in vitro model using E. 
coli ATCC 35218 and the same conditions described above for a constant concentration. 
Four different initial concentrations were investigated: 8, 16, 32 and 64 |ig/mL. Samples 
were withdrawn at time zero (time of drug injection into the system), 0.5, 1, 1.5, 2, and 
2.5 hours. The stability of PIP in combination with TZB was also investigated in the same 
conditions. Piperacillin (8 ng/mL) was combined with TZB 4 ng/mL (1 :2), 2 ^g/mL 
(1 :4), and 1 ng/mL (1 :8). Samples were collected at time 0, 1, 2, 4, 6, 8, 10, and 24 
hours. All samples were analyzed by HPLC using the conditions described in Chapter 3. 
Three experiments were conducted for each case. The bacterial counting was determined 
in each experiment. A negative control with the bacteria in the absence of drugs was also 
included to assure that the inoculum was active. 

TZB Minimum Effective Concentration 

In general, P-lactam and P-lactamase combinations are used in only one fixed dose 
ratio. Tazobactam and piperacillin are administered to patients in two dose ratios: 1 :4 and 
1:8. Some experiments were conducted to investigate if these two ratios have the same 
efficacy in vitro as well as the minimum ratio of TZB in combination with PIP that still 
produces an antiinfective activity. Concentration ratios were investigated instead of dose 



75 



ratios. The concentration of PIP used is in the same order of magnitude of free levels of 
the drug expected at steady state after constant intravenous infiision obtained with current 
therapy. The concentrations of PIP and TZB were kept constant throughout the 
experiments. One single concentration of PIP was used (8 |ag/mL) for all experiments. 
The concentration of TZB was 4 |ig/mL for the first experiment and it was decreased by a 
factor of 2 up to 15 ng/mL for each subsequent experiment. In this way the concentration 
ratios investigated ranged from 1 :2 to 1 :5 12. Samples were withdrawn for bacterial count 
at time zero (right before drug addition to the in vitro model following two hours of 
incubation), 1, 2, 4, 6, 8, 12, and 24 hours. The negative controls were bacteria in the 
absence of any drug and bacteria in the presence of TZB 4^g/mL. For the positive control 
PIP alone 8ng/mL was used. Each experiment was repeated on a different day. 

Experimental Design 

Piperacillin and tazobactam kinetics in human 

Piperacillin is reported to have a dose-dependent pharmacokinetics in the dose 
range used for therapy. For this reason the concentrations simulated in this study were 
calculated to be in the same order of magnitude as it would be expected assuming its non- 
linear behavior. For the simulation of concentration-time profiles of free piperacillin and 
tazobactam in human tissue following multiple i.v. bolus administrations parameters 
estimated from fitting plasma data to a two-compartment model were used in the same 
equation presented in Chapter 4 (eq. 4-4). All the pharmacokinetic parameters were taken 
from Bergan and Williams (1 1) and are presented in Table 5-1. The parameters shown for 
the dose 30 mg/kg were used to calculate the free concentration-time profile for the 
lowest dose of PIP (2g) simulated in vitro. The parameters shown for 60 mg/kg were 
used to predict free tissue concentration-time profiles for 4 and 8 g of PIP. For the 
prediction of free tissue levels after constant intravenous infiision, different clearances had 



76 . . 

to be used since it was reported in the literature that PIP clearance decreases with 
increasing dose. The clearance values used were taken from Tjandramaga et al. (1978) 
based on similar total daily dose (15). For the inflision rates 30, 60, and 120 mg/h of PIP 
the value used for clearance was 24.52 L/h. For the infusion rate 240 mg/h the value used 
for clearance was 18.11 L/h. The fraction unbound used for PIP was 0.79 in all cases (9). 



Table 5-1. Piperacillin pharmacokinetic parameters used for the simulations of 
concentration-time profiles in human tissue after i.v. administration of 
piperacillin and tazobactam combinations. 



Dose (mg/kg) 


A (jig/mL) 


B (fig/mL) 


a (h-1) 


3 (h-l) 


30 


158.03 


78.83 


3.847 


0.677 


60 


316.76 


205.69 


6.385 


0.782 


From Bergan anc 


Williams (1982) (11). 



Pharmacokinetic parameters derived from concentration-time profiles obtained 
after administration of TZB (375 mg) combined with PIP (3 g) in heahhy volunteers were 
used for the prediction of tazobactam free tissue levels after i.v. bolus administration as 
well as after constant intravenous inflision. The parameters are shown in Table 5-2 and 
were obtained from Cyanamid - Germany (Study # 68-37 - A multiple dose, open label, 
non-comparative, parallel, multi-center, pharmacokinetic study of piperacillin and 
tazobactam after 30 min intravenous infusion in subjects with various degrees of renal 
impairment). The value used for clearance was 14.45 L/h for all the inflision rates studied. 
The fraction unbound used for TZB was 0.79 (8). 



Table 5-2. Tazobactam pharmacokinetic parameters used for the simulations of 
concentration-time profiles in human tissue after i.v. administration of 
piperacillin and tazobactam combinations. 



Dose (mg) 


A (^g/mL) 


B (^g/mL) 


a (h-1) 


3 (h-1) 


375 


21.53 


18.33 


3.61 


0.91 



77 



Simulation of constant intravenous infusion 

For the simulation of constant intravenous infusion PIP and TZB concentration at 
steady state were calculated using eq. 5-1 : 



_ ko 



where ko is the infusion rate constant and CL is the total body clearance. The free 
concentrations were obtained by using the fraction unbound for each drug. In order to 
facilitate the preparation of solutions, rounded figures were used. The actual 
concentrations simulated for PIP and TZB are shown in Table 5-3. 



Table 5-3. Piperacillin and tazobactam free tissue concentrations at steady state after 
constant intravenous infusion. 



PIPko 
(mg/h) 


30 


60 


120 


240 




PIP Cpss 
(^g/mL) 


1 


2 


4 


10 




TZB ko 
(mg/h) 


3.75 


7.5 


15 


30 


60 


TZB Cpss 
(^g/mL) 


0.25 


0.5 


1 


2 


4 



All the combinations that produced dose ratios TZB-PEP 1 :4 and 1 :8 with these 
infusion rates were investigated. The drug concentrations in the in vitro model were kept 
constant throughout the experiment. Samples for bacteria counting were withdrawn at 
time zero (before drug administration), 1, 2, 4, 6, 8, 12, and 24 hours. Each experiment 
was conducted in duplicate. 



78 



Simulation of i.v. bolus multiple dosing 

Monoexponential kinetics was used for the in vitro simulation of free drug 
concentrations after i.v. bolus administration. Three doses of PIP (2, 4 and 8 g) combined 
with TZB (0.5 g), dose ratios 1:4, 1:8 and 1:16, were simulated in the in vitro model of 
infection. The maximum free concentration in tissue after i.v. bolus administration is 
obtained at Xxn&x- The time for maximum concentration in the peripheral compartment of 
a two-compartment model can be calculated using eq. 5-2: 



In 



max a_p 



(5-2) 



where a and (3 are the hybrid constants for the distribution and elimination phases, 
respectively. The value of t^ax was calculated for each dose of each drug using the 
parameters presented in Tables 5-1 and 5-2. Using tmax' the corresponding C^ax of free 
piperacillin and tazobactam in the tissue for various dosing regimens after the first dose 
was calculated using eq. 4-4. Table 5-4 displays the results. For piperacillin calculations 
dose dependency was assumed as it was mentioned before. 



Table 5-4. Maximum fi-ee concentrations of piperacillin and tazobactam in the tissue for 
difierent doses after administration of the first i.v. dose. 



Dose (g) 


PIP 2 


PIP 4 


PIP 8 


TZB 0.5 


Cmax (^ig/mL) 


50 


150 


300 


16 



The concentrations displayed in Table 5-4 were added to the in vitro model at time 
zero and at specific times depending on the dose interval being investigated in the 
experiment. A monoexponential decline with a half-life of one hour after C^ax had been 
reached was simulated. The distribution phase from central to peripheral compartment 



79 



was not simulated due to limitations of the model used. Since the distribution phase was 
relatively short it was assumed that it would not influence significantly the outcome of the 
experiments. 

Four different dosing regimens were simulated for each one of the doses studied: 
once a day administration (q24h), twice as day administration (ql2h), three times a day 
administration (qSh), and four times a day administration (q6h). Samples for bacteria 
counting were withdrawn at time zero (before drug administration) and every two hours 
up to twenty-four hours. For the negative control, the number of bacteria was determined 
in absence of any drug. For the positive controls the number of bacteria was determined 
in the presence of piperacillin 2, 4 and 8 g alone. Each experiment was repeated on a 
different day. Piperacillin concentrations was determined for all three doses alone and in 
combination in the q6h experiment. 

In another set of experiments, PIP (8 g) was combined with higher concentrations 
of TZB, 64 and 256 ng/mL corresponding to 2 and 8 g, respectively, in a ql2h simulation. 
Samples for bacteria counting were taken at the same time points specified above. 
Piperacillin concentrations were determined for both combinations. Each experiment was 
repeated on a different day. 

The average results of the piperacillin concentration-time profiles were fitted to a 
monoexponential equation using the computer program SCIENTIST (Micromath, Salt 
Lake City, UT). 



80 

Results 



Comparison Between Human Tissue Levels and In Vitro Levels 

The results of the in vitro levels for PEP and TZB using a stepwise dilution method 
are shown in Figure 5-1. It can be seen that in the absence of bacteria in the system, the 
dilution method is able to reproduce the desired levels for both drugs with very good 
accuracy. In this way, the half-life of both drugs can be simulated in vitro using the 
proposed infection model. 

Piperacillin Stability In The In Vitro Model 

The results of the stability of constant concentrations of piperacillin alone in the 
presence of coli are shown in Figure 5-2. It can be seen that for the two lower 
concentrations, 8 and 16 ng/mL, a monoexponential equation can be used to fit the data 
with a degradation rate constant (kp) of 0.712 h"!. The half-life calculated for both 
concentrations is 58 min. For the two higher concentrations, 32 and 64 ng/mL, a small 
degree of nonlinearity could be detected. The data could be fitted to a nonlinear equation 
with a Michaelis-Menten constant (Km) of 20.8 jig/mL and the maximum rate of reaction 
(^max) of 33.5 ^ig/h. However, when the two higher concentrations were fitted to a 
linear equation the degradation rate constants 0.802 hr^ and 0.539 h'^ were obtained for 
PIP 32 and 64 ng/ml, respectively. The MSC and correlation coefficient for this fit were 
still very good, 2.70 and 0.98, respectively. 

The pharmacodynamic effect measured for these four concentrations is displayed 
in Figure 5-3. It can be observed that the killing effect is more pronounced with 
increasing the concentration. The two lower concentrations showed an effect of short 
duration and regrowth occurred after three hours. The other two concentrations, 32 and 
64 ng/mL produced a more prolonged effect, showing regrowth after four hours. 



81 



105 T 




2 4 6 8 

Time (h) 

Figure 5-1. Comparison between levels of piperacillin (•) and tazobactam (■) measured 
by HPLC in the in vitro model of infection and levels calculated from human 
pharmacokinetics (lines) using broth solution (upper panel) or phosphate 
buffer 5 mM (lower panel). Mean ± SD of 3 experiments. 



82 




Figure 5-2. Piperacillin stability in the in vitro model in the presence of E. coli ATCC 
35218 for four different initial concentrations: 8 ng/mL (■), 16 ^g/rnL (•), 
32 ng/mL (♦) and 64 ng/mL (A). Mean ± SD of 3 experiments. 




w -I 
102 -, 

10' T 

10° n 1 1 ' 1 1 1 1 1 1 1 1 1 r 



2 4 6 8 

Time (h) 

Figure 5-3. Number of bacteria as a function of time for four initial concentrations of 
piperacillin alone: 8 ng/mL (■), 16 ng/mL (•), 32 ng/mL (♦), and 64 ^g/mL 
(A). Negative control in the absence of drug (□). Mean ± SD of 3 
experiments. 



83 



The results of the stability studies with PIP (8 \ig/mL) combined with TZB (1 :2 to 
1 :5 12) are shown in Figure 5-4. The data was fitted to a monoexponential equation. The 
PIP half-life was estimated to be 41 h when combined with TZB 4 ^g/mL (1 :2), 26 h with 
TZB 2 [ig/mL (1 :4), and 20 h with TZB Ijig/mL (1 :8). Comparing these half-lives with 
the half-life of PIP alone in the same concentration (58 min) it can be concluded that TZB 
is protecting piperacillin from the degradation caused by the P-lactamase. 

TZB Minimum Effective Concentration 

The results of the pharmacodynamic effect of piperacillin (8 |ig/mL) combined 
with tazobactam in different ratios are shown in Figure 5-5. The concentration ratios 
investigated varied from 1:2 to 1:512. Tazobactam alone 4 ng/mL did not produce any 
killing effect. As was shown previously, PIP alone (8 |ig/mL) produced an effect of short 
duration. The most effective killing was obtained with the combination of 4 ^g/mL of 
TZB (1 :2). No regrowth was observed up to twenty-four hours. The concentration ratio 
1 :4 also showed a very effective killing, maintaining the number of bacteria below the limit 
of quantification for up to twenty-four hours. The ratio 1 :8 showed a less pronounced 
effect being able to control the bacterial level for up to twelve hours only. From this ratio 
on, the lower the concentration of TZB in the system, the less pronounced was the PIP 
effect and the faster was the bacterial regrowth. 

By increasing the concentration of TZB in combination with a fixed concentration 
of PIP it was possible to prolong the stability of piperacillin from a half-life of 
approximately one hour (PIP 8 ng/mL alone) to a half-life of forty hours (PIP combined 
with TZB 4 ^ig/nlL - 1 :2). The increase in piperacillin half-life is reflected in its killing 
effect against E. coli. With lower concentrations of P-lactamase inhibitor in combination, 
the protective effect of TZB is shorter because its small amount is rapidly inactivated by 
the P-lactamase which is then available to interact v^th PIP. Thus, the more effective 



84 




Time (h) 

Figure 5-4. Piperacillin (8 lig/mL) stability in the in vitro model combined with 
tazobactam 1 ng/mL (A), 2 |ig/mL (•), and 4 ng/mL (■). Mean ± SD of 3 
experiments. 



combination is the one that supplies enough TZB to inhibit the P-lactamase for longer 
periods of time increasing the probability of PIP to penetrate the bacterial periplasmic 
space and interact with the penicillin binding proteins to produce the killing effect. 

Simulation of Constant Intravenous Infusion 



The pharmacodynamic effects of constant piperacillin concentrations combined 
with tazobactam in different ratios simulating in vivo levels obtained in human tissue after 
constant i.v. infusion are displayed in Figures 5-6 and 5-7. It can be seen in Figure 5-6 
that for PIP infusion rate 30 mg/kg (1 ng/mL) combined with TZB 3.75 mg/kg (0.25 
Hg/mL) or TZB 7.5 mg/kg (0.5 ng/mL) the number of bacteria was initially decreased by 
two-log scale but regrowth was observed after four and six hours, respectively. 



85 



lO'O -f 




102 1 



10' 1 

10^ I I ' ' I I I — ' 1 1 1 1 1 1 1 1 1 1 r — -1 1 1 1 1 1 — 

5 10 15 20 25 

Time (h) 

Figure 5-5. Number of bacteria as a function of time after administration of piperacillin (8 
Hg/mL) alone (■) or combined with TZB: 15 ng/mL (□), 30 ng/mL (•), 60 
ng/mL (O), 125 ng/mL (♦), 250 ng/mL (❖), 500 ng/mL (A) (upper panel) 
and, 1 ng/mL (A) 2 ng/mL (□), and 4 |ig/mL (■) (lower panel). Negative 
control in the absence of any drug (*) and with TZB (4 ng/mL) alone (x - 
dotted line). Mean ± SD of 2 experiments. 



86 



Increasing the infusion rate of PIP to 60 mg/kg (2 ng/mL) a more effective killing effect 
was observed for all three dose ratios investigated. The number of bacteria was kept 
constant for up to eighth hours for the two higher ratios (1:4 and 1:8) but regrowth was 
observed afler four hours for the lowest proportion of TZB in combination (1:16). Figure 
5-7 shows that further increase in PIP infiision rate to 120 mg/kg (4 \xg/mL) did not 
produce more pronounced killing although bacterial regrowth was only observed after 
eight hours for the combination of TZB 1:8. For the ratio 1 :4, TZB concentration of 2 
|ig/mL, a plateau was observed up to eight hours but no regrowth was visible up to 
twenty four hours. For PIP 240 mg/kg (10 ng/mL) combined with TZB 1 :8 (2 ^g/nlL) 
the same pattern shown for PEP 120 mg/kg (1 :4) was observed. The most effective killing 
was observed for PEP 240 mg/kg combined with TZB 60 mg/kg (4 ^g/mL). The number 
of bacteria was below the limit of quantification (10^ CFU/mL) after one hour and except 
for a count at 8 h no regrowth was observed up to twenty-four hours. In this way, the 
maximum pharmacodynamic effect was obtained for E. coli in this in vitro model. Further 
increase in piperacillin and tazobactam concentrations will not produce any increase in 
effect. 

It is important to emphasize that although the goal of the constant infusion 
simulations in vitro was to keep the concentrations of both drugs constant throughout the 
experiment, the concentration of PIP was shown to decrease because of the interaction 
with the P-lactamase produced by the bacteria. With lower concentrations of both drugs 
the degradation rate constant should be bigger than the one estimated for PIP 8 ng/mL 
combined with TZB 1 , 2 and 4 |ig/mL. The change in PIP levels has to be taken into 
account for the PK-PD modeling. 



87 




103 -| 
102 1 



10*^ I I I I 1 — I 1 1 1 1 — 1 — I 1 1 1 1 1 r~ — I 1 1 1 1 1 — 

5 10 15 20 25 

Time (h) 

1010 1 




5 10 15 20 25 

Time (h) 

Figure 5-6. Number of bacteria as a function of time for simulation of constant infusion 
rates of piperacillin and tazobactam. Closed symbols represent TZB-PEP dose 
ratio 1:4 and open symbols represent dose ratio 1:8. Upper panel : PIP 30 
mg/kg and TZB 7.5 mg/kg (1:4) or TZB 3.75 mg/kg (1:8); Lower panel: PIP 
60 mg/kg and TZB 15 mg/kg (1:4) or 7.5 mg/kg (1:8) or 3.75 mg/kg (1:16) 
(x). Negative control in the absence of drugs (*). Mean ± SD of 2 
experiments. 



88 



lO'O T 




102 



10' -[ 

IQO 1 — I — I — I — I — I — I — I — I — I — r~T — 1 — I — [ — I — I — I — I — I — I — I — 1 — I — 

5 10 15 20 25 

Time (h) 



IO'Ot 




102 -5 



101 -| 

10" ~] I I I — I — I — ' — I — I — I — I — 1 — I — I — I — I — 1 — I — I — I — I — I — I — I — I — 
3 10 15 20 25 

Time (h) 

Figure 5-7. Number of bacteria as a function of time for simulation of constant infusion 
rates of piperacillin and tazobactam. Closed symbols represent TZB-PIP dose 
ratio 1:4 and open symbols represent dose ratio 1:8. Upper panel: PIP 120 
mg/kg and TZB 30 mg/kg (1:4) or 15 mg/kg (1:8); Lower panel: PIP 240 
mg/kg and TZB 60 mg/kg (1:4) or 30 mg/kg (1:8). Negative control in the 
absence of drugs (*). Mean ± SD of 2 experiments. 



89 



Simulation of i.v. Bolus Multiple Dosing 

Determination of piperacillin concentration 

The concentrations of piperacillin alone (2, 4 and 8 g) determined for the control 
experiments in simulations of q6h dosing regimen are shown in Figure 5-8. The mean data 
for the three doses was simultaneously fitted to a one exponential equation using 
SCIENTIST. The resulting elimination rate constant was 1.423 h"l which represents a 
half-life of approximately 30 min. 

103 T , 




2 4 6 8 10 12 

Time (h) 

Figure 5-8. Piperacillin concentrations in simulations of i.v. bolus multiple dosing of 2 g 
(■), 4 g (•), and 8 g (A) q6h. Mean ± SD of 2 experiments. 



Piperacillin concentrations were also determined in the q6h simulations for the 
three doses studied (2, 4 and 8 g) combined with same dose of TZB (0.5 g), as well as in 
the ql2h studied using higher doses of TZB in combination with PIP 8 g. Figure 5-9 



90 



105 T 




2 4 6 8 10 12 



Time (h) 

103 T 




Time (h) 

Figure 5-9. Piperacillin concentrations in simulations of i.v. bolus multiple dosing. Upper 
panel: PIP 2 g (■), 4 g (•), and 8 g (A) combined with TZB 0.5 g q6h. 
Lower panel: PIP 8 g combined with TZB 2 g (•) and 8 g (■). Means ± SD 
of 2 experiments. 



91 



displays the results for these two experiments. The average concentration-time profiles 
were fitted to a monoexponential equation. Simultaneous fit was performed for the three 
different doses of PIP when combined with the same dose of TZB. The elimination rate 
constant obtained was 0.905 h"! which corresponds to a half-life of 46 min. In the same 
way, simultaneous fit was performed for the two different doses of TZB when combined 
with the same dose of PEP. The elimination rate constant obtained for this case was 0.819 
h'^ which corresponds to a half-life of 51 min. 

In all muhiple doses studies in vitro the dilutions were designed to produce a half- 
life of one hour. The discrepancies between the simulated half-life using stepwise dilution 
and the observed ones are due to degradation of piperacillin by the P-lactamase produced 
by the bacteria. Subtracting the dilution rate from the obtained elimination rate constant, 
one obtains the degradation rate constant of piperacillin in each case. The degradation 
rate constant of PIP in the absence of TZB is 0.73 h"^. PIP degradation rate constants are 
0.212 h"l and 0. 126 h'^ for the lower and higher proportion of TZB in combination, 
respectively. The difference observed in the rate constants demonstrate the role of TZB in 
this combination, protecting PIP from degradation which allows for this antibiotic to be 
present in higher concentrations at the site of action. Higher proportions of TZB in 
combination produce more effective protection of PIP. This is reflected in the different 
degradation rates estimated. Piperacillin half-life observed when combined with the higher 
proportions of TZB is very similar to the one simulated by dilution showing that the 
maximum inhibition of the P-lactamase was reached. 
Pharmacodynamic effect 

The pharmacodynamic effect of PIP alone against E. coli in simulations of i.v. 
bolus multiple dosing of 2, 4 and 8 g every six hours is shown in Figure 5-10. 

It can be seen that all doses produced a similar effect reducing the number of 
bacteria by a two-log scale in the first two hours. After that, regrowth was observed in a 



92 




102 -| 
10' 1 

IQO 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 — 

2 4 6 8 10 12 

Time (h) 

Figure 5-10. Number of bacteria as a flinction of time after administration of piperacillin 
alone 2g(>), 4g(«), and 8 g (♦) every six hours. Negative control in the 
absence of antibiotic (A). Mean ± SD of 2 experiments. 

dose dependent fashion. The administration of the second dose did not have a significant 
effect on the regrowth of the bacteria for PIP 2 g experiment because after six hours the 
number of bacteria was already greater than the initial inoculum. For the intermediate 
dose (4 g) the second administration of piperacillin produced the same initial effect but 
regrowth was resumed after two hours. Piperacillin 8 g showed a more persistent effect 
than the other two doses. The second administration after six hours produced a ftjrther 
decrease in bacterial counts. The number of bacteria was maintained below the initial 
inoculum at all times. 

The pharmacodynamic effect of PIP-TZB against E coli in in vitro simulations of 
i.v. bolus multiple dosing is displayed in Figures 5-11 to 5-14. Simulations of the actual 
free tissue levels of piperacillin observed in the model (46 min half-life) and expected 
levels of TZB (60 min half-life) are shown together with the pharmacodynamic results. 



93 




Figure 5-11. Upper panel: Number of bacteria as a function of time after once a day 
administration of piperacillin 2 g (■), 4 g (•), and 8 g (♦) combined with 
tazobactam 0.5 g. Negative control in absence of drug (A). Lower panel: 
Concentration time profiles simulated for piperacillin (solid line) and 
tazobactam (dashed line) in the in vitro model of infection for the dosing 
regimens specified above. Mean ± SD of 2 experiments. 



94 




102 T 
10' 1 

10" 1 1 1 1 1 1 1 1 1 1 1 T~~l 1 1 ' 1 1 1 1 1 1 1 1 

5 10 15 20 25 

Time (h) 

300 -I 1 




Time (h) 

Figure 5-12. Upper panel: Number of bacteria as a function of time after twice a day 
administration of piperacillin 2 g (■), 4 g (•), and 8 g (♦) combined with 
tazobactam 0.5 g. Negative control in absence of drug (A). Lower panel: 
Concentration time profiles simulated for piperacillin (solid line) and 
tazobactam (dashed line) in the in vitro model of infection for the dosing 
regimens specified above. Mean + SD of 2 experiments. 



95 




Time (h) 




Time (h) 



Figure 5-13. Upper panel: Number of bacteria as a function of time after three times a day 
administration of piperacillin 2 g (■), 4 g (•), and 8 g (♦) combined with 
tazobactam 0.5 g. Negative control in absence of drug (A). Lower panel: 
Concentration time profiles simulated for piperacillin (solid line) and 
tazobactam (dashed line) in the in vitro model of infection for the dosing 
regimens specified above. Mean ± SD of 2 experiments. 



96 



lO'O T 




102 -| 
101 1 



10" I ' I I I I I I I I I — I — 1 — I — I — I — I — I — I — I — I — I — I — I — I — 
5 10 15 20 25 

Time (h) 



300 




5 10 15 20 25 

Time (h) 



Figure 5-14. Upper panel: Number of bacteria as a function of time after four times a day 
administration of piperacillin 2 g (■), 4 g (•), and 8 g (♦) combined with 
tazobactam 0.5 g. Negative control in absence of drug (A). Lower panel: 
Concentration time profiles simulated for piperacillin (solid line) and 
tazobactam (dashed line) in the in vitro model of infection for the dosing 
regimens specified above. Mean + SD of 2 experiments. 



97 



Figure 5-11 shows the pharmacodynamic effect after once a day administration. 
The three doses investigated showed similar killing effect but regrowth was observed after 
six or eight hours in all cases. For q24h the initial concentrations are very high in the 
beginning of the experiment but drop to almost zero at the end of the interval. After 6-8 
hours bacterial regrowth occurs due to low concentrations of piperacillin and tazobactam. 
The same behavior can be observed in Figure 5-12 for twice a day administration. The 
regrowth observed after eight hours was slowed with the second dose but bacterial levels 
were higher than observed after the first dose. With the second dose regrowth was 
observed after 18-20 hours. A more effective killing was observed for all three doses 
administered every eight hours (Figure 5-13). With the second and third doses, the 
number of bacteria was below the limit of quantification at almost all dosing intervals. 
Administration of PIP-TZB every six hours (Figure 5-14) showed an overall effect similar 
to the one observed for three times a day schedule. After the third dose, bacterial counts 
were below the limit of quantification up to twenty-four hours. 

Comparing the dosing intervals investigated one can conclude that the once a day 
administration of PEP-TZB combinations is not effective enough to suggest this dosing 
regimen for therapy. Two times a day administration seems to be insufficient as well. 
Although the administration of the second dose still produces some killing its effect is not 
as pronounced as the first dose and a very high bacterial density is observed in the end of 
the second dosing interval. Administration of all doses studied every 6 or 8 hours seems 
to keep the number of bacteria within a more restricted range. These two dosing intervals 
appear to be equally effective in eradicating E. coli in vitro. As was pointed out before, 
for the simulations of constant intravenous infusion, there seems to be an upper limit to 
the pharmacodynamic effect which can not be enhanced by further increases in PIP dose. 
For all the cases investigated, the three doses of piperacillin showed a very similar effect. 
What seems to be important in all cases is the concentration of TZB present. Since all 
three doses of PIP were combined with the same dose of TZB the protective effect of this 



98 



dmg was similar in all cases. It could be inferred that an increase in the TZB dose would 
increase the duration of the maximum effect observed for piperacillin. The results of the 
administration of the higher dose of PEP (8 g) combined with higher proportions of TZB 
ql2h validate this assumption (Figure 5-15). In the presence of increased 

1010 1 




101 

10" ~i ' I I — I — I — I — I — I — I — I — I — I — 1 — I — I — I — I — 1 — I — I — I — I — 1 — I — 

5 10 15 20 25 

Time (h) 

Figure 5-15. Number of bacteria as a function of time after administration of piperacillin 8 
g combined with tazobactam 2 g (■) and 8 g (•) every twelve hours. 
Negative control in the absence of drugs (A). Mean ± SD of two 
experiments. 

concentrations of TZB, a slightly more pronounced initial killing is observed and the effect 
persists longer. Regrowth occurs after ten hours as opposed to the regrowth after eight 
hours observed for the lower concentration of TZB in combination (Figure 5-12). In this 
way, the second administration of the drugs is more effective when higher proportions of 
TZB are present in the combination. The number of bacteria was below the LOQ for most 



99 

of the second dosing interval which differs completely from the results obtained when a 
lower concentration of TZB was present. A similar effect was observed for the two 
higher doses of TZB (2 g and 8 g) in combination with PIP leading to the conclusion that 
when enough TZB in present in the in vitro model the effect of PIP can be maximized and 
consequently the dosing interval can be prolonged. 

Conclusions 

The pharmacodynamic effect of piperacillin alone and in different combinations 
with tazobactam was investigated in vitro against bacteria that produce P-lactamase. In 
this scenario, PIP stability is dependent on the activity of the hydrolyzing enzyme and on 
the concentration of TZB in the system. Piperacillin alone showed a killing effect of short 
duration and less effective than the one observed when combined wdth the P-lactamase 
inhibitor. As expected, higher proportions of TZB in combination increased the half-life 
of PIP which leads to a more prolonged effect against the bacteria. A maximum killing 
effect can be obtained in simulations of constant as well as fluctuating concentrations of 
both drugs. In this situation, an increase in the concentration of PIP did not produce a 
more pronounced killing effect. Further increases in the proportion of TZB in the 
combination increases the time that PIP can interact with the penicillin binding proteins in 
the site of action, producing a more prolonged and pronounced effect. Whether the 
changes in PIP concentrations observed in the in vitro experiments are also significant at 
the infection site in vivo needs to be investigated. Furthermore, how these changes affect 
the pharmacokinetics in humans, if any change can be observed, also needs to be 
investigated. However, the different concentrations observed in the in vitro model 
compared to the expected ones have to be taken into account when designing a 
pharmacokinetic-pharmacodynamic model. 



CHAPTER 6 

PHARMACOKINETIC-PHARMACODYNAMIC MODELING 

Specific Aims of the PK-PD Modeling 

The specific aims of the PK-PD modeling were to correlate mathematically the 
pharmacokinetic parameters observed in humans for different combinations of piperacillin 
and tazobactam with the pharmacodynamic effect observed in vitro against E. coli 
(PK/PD model), to compare different doses and dosing regimens of the combinations of 
piperacillin and tazobactam using the derived PK/PD model, and to use the model 
obtained to validate the hypothesis that piperacillin combined with tazobactam can be 
administered less fi-equently without loss of efficacy. 

A PK-PD model is frequently devised with the intention of making predictions of 
the expected effect for a given dose and dose regimen. A modified E^^y^-moM was used 
in a previous study with piperacillin alone in order to predict the changes in the number of 
bacteria as a fiinction of time for any given dose of this antibiotic (4). The effect in this 
model is measured as the inhibition of bacterial growth rate or killing (reduction of number 
of bacteria). In a first attempt to model the data obtained for PIP combined with TZB, the 
same model was used. The advantage of the E^ax-model is that it predicts no effect in 
the absence of drug and a maximum effect when the drug concentrations are very high. 
This model seems suitable for the interaction of p-lactam antibiotics and bacteria since it is 
reported that increases in concentration 4-5 times above the MIC do not produce a 
significant increase in the killing effect (2). 



100 



101 



The experimental data was fitted to the following model using the non-linear least- 
square regression program SCIENTIST (4): 



dN 
dt 



k C 

_ max 



•N 



(6-1) 



where dN/dt is the change in number of bacteria as a function of time (pharmacodynamic 
effect), k (h-1) is the bacteria generation rate constant in the absence of any drug, kj^^x 
(h-1) is the maximum killing effect, C (ng/mL) is the concentration of PIP at time t, and 
EC50 (^g/mL) is the concentration of PIP required to produce 50% of the maximum 
effect. In absence of drug bacteria growth at their normal grow rate and the term 
(kmax C)/(EC5o+C) equals zero. In the presence of high drug concentrations, killing is 
induced. With C much higher than EC 59, the term C in the equations cancels out and the 
resultant kill rate is k-k^ax- 

As was shown in Chapter 5 the concentration of PEP in the in vitro system is 
dependent on the concentration of TZB in the combination. Even when a constant 
infusion was simulated, the concentration of PIP was not constant due to degradation by 
the p-lactamase. In order to model the effect as a function of time, the decHne in 
piperacillin concentrations was taken into account by using a monoexponential equation 
with the elimination rate constant (kp) obtained from experimental PIP concentrations. 
When no data was available for the PIP concentrations in that specific combination, the 
elimination rate constant was estimated by fitting the pharmacodynamic data. 

An initial fit was performed simultaneously for the control (no drugs) and each of 
the PIP-TZB combinations in simulations of i.v. bolus multiple dosing. The average 
values obtained for k and k^ax were 1.54 ± 0.21 h"! (range 1.27 to 1.84 h'l) and 3.87 ± 
0.74 h-1 (range 3.05 to 5.89 h'l), respectively. These numbers are similar to the values 
obtained for piperacillin alone in our previous study: k of 1.50 ± 0.56 h"! and kma^ 3.19 + 



102 



1 .39 h"^ (4). The bacterial growth rate (k) is constant for a bacteria in specified 
conditions. The maximum killing effect (kmax) is also constant for a specific antibiotic. 
Furthermore, the addition of tazobactam did not affect kj^^x- ^ o'" these reasons k (1.54 
h"l) and kj^^x (3.87 h"l) were kept constant for data analysis. In this way the 
interdependence of EC50 on k^^y^ can be eliminated and the values obtained for EC50 
can be better compared for all doses and dosing intervals investigated. All the data points 
were weighted equally for the fits using a weighting factor of 1 . 

PK-PD Analysis for Piperacillin alone 

The pharmacodynamic data obtained for piperacillin alone against E. coli in 
simulations of constant infusions as well as i.v. bolus multiple dosing were fitted using the 
model described above. For simulations of constant infusion four initial concentrations 
were investigated: 8, 16, 32 and 64 |ag/mL. However, due to the degradation of PIP, 
concentrations in these undiluted experiments will not remain constant, but decrease. The 
linear elimination rate constants determined fi-om measured piperacillin concentrations in 
the same experiments, as shown in Chapter 5, were used. For simulation of i.v. bolus 
multiple dose q6h three doses were investigated: 2, 4 and 8 g corresponding to initial 
concentrations of 50, 150 and 300 |ag/mL of piperacillin. The elimination rate constant 
used in this case was 1.423 h"!. As pointed out in Chapter 5 this elimination rate constant 
represents the sum of the dilution processes (0.693 h"!) and the degradation of PIP by the 
p-lactamase. Hence, the value of 1.423 h"^ is equivalent to a degradation rate constant of 
0.73 h-1. Figure 6-1 and 6-2 display the results for the effect of undiluted and fluctuating 
PIP concentrations, respectively. The results of the curve fits for all the cases where 
piperacillin was administered alone are shown in Table 6-1. 



103 




Time(h) 



TimeOi) 





Time (h) 



Figure 6-1. Curve fit for control (*) and for piperacillin alone 8 \ig/mL (■), 16 |ig/mL 
(•), 32 ng/mL (♦), and 64 ^g/mL (A). Error bars indicate SD. 



Table 6-1. Results of curve fits for piperacillin alone. 



PEP concentration 
Dosing Regimen 


ECso (Mg/mL) 


r2 


MSC 


8 [ig/mL - infusion 


16.78 


0.98 


2.41 


16 ng/mL - infusion 


5.62 


0.97 


2.24 


32 ^g/mL - infiision 


5.82 


1.00 


4.33 


64 ng/mL - infiision 


12.18 


1.00 


4.33 


2 g (50 ug/mL) q6h 


5.40 


0.67 


0.20 


4g(150 Ug/mL) q6h 


5.97 


1.00 


4.73 


8 g (300 Ug/mL) q6h 


5.62 


1.00 


4.74 


Average 


8.20 + 4.50 







104 




Figure 6-2. Curve fit for control (*) and piperacillin 2 g (■), 4 g (•), and 8 g (♦) every 
six hours. Error bars indicate SD. 



105 



Very good fits were obtained for all cases using the measured PIP concentrations. 
The average EC50 for all the situations where PIP was administered alone was 8.20 ± 
4.50 ng/mL. 

Effect of Tazobactam Concentration 

In this set of experiments, a fixed concentration of PIP (8 ng/mL) was combined 
with different concentrations of TZB in the concentration ratio 1:2 to 1:512. An initial 
attempt was made to fit the pharmacodynamic effect of PIP combined with TZB (1,2, and 
4 ng/mL) using the elimination rate constants obtained from measured concentrations of 
PIP in those experiments. The values for the elimination rate constants previously 
reported in Chapter 5 are 0.017 h"!, 0.027 h'l, and 0.034 h"! for TZB-PIP concentration 
ratios 1 :2, 1 :4 and 1 :8, respectively. The curve fits obtained for these ratios are displayed 
in Figure 6-3 and the respective parameters are listed in Table 6-2. 



Table 6-2. Results of the curve fits for piperacillin 8 \ig/mL combined with tazobactam in 
different ratios using elimination rate constants calculated based on piperacillin 
concentrations measured in vitro. 



Concentration 
(Hg/mL) 
(Ratio) 


EC50 
(Mg/mL) 




MSC 


TZB 4 (1:2) 


0.90 


1.00 


0.71 


TZB 2 (1:4) 


0.77 


1.00 


0.76 


TZB 1 (1:8) 


1.54 


1.00 


0.82 



Although the fits are good for the higher concentrations of TZB in combination, 
the model was not capable of fitting the bacterial regrowth observed for the lower 
concentration (1 |ig/mL to 15 ng/mL). Furthermore, comparing the degradation rate 
constants it seems clear that the stability of PIP is dependent on the concentration of TZB 



106 




Figure 6-3. Curve fit for control (■) and for piperacillin (8 ng/mL) combined with 
tazobactam 1 \ig/mL (•), 2 ^g/mL (♦), and 4 ng/mL(A). Error bars 
indicate SD. 



107 



present in the system. Higher concentrations of TZB produce more protection from 
degradation by the P-lactamase. Since the model was not capable of describing the 
data,the analysis was redone using kp (PIP degradation rate constant) as a second 
parameter besides the EC50. Using this approach the pharmacodynamic effect is used to 
model the pharmacokinetics of PIP in the in vitro system. 

The resulting curve fits for PIP 8|ig/mL alone and combined with different 
concentrations of TZB (4 ng/mL to 15 ng/mL) were significantly improved and are 
displayed in Figure 6-4. Each drug combination ratio was fitted individually. Table 6-3 
displays the respective parameters. 



Table 6-3. Results of the curve fits for piperacillin 8 pg/mL combined with tazobactam in 
different ratios. 



Concentration 
(Hg/mL) 
(Ratio) 


kp 
(h^) 


EC50 
(^g/mL) 




MSC 


TZB 4 (1:2) 


0.13 


0.94 


1.00 


0.46 


TZB 2 (1:4) 


0.12 


0.77 


1.00 


0.76 


TZB 1 (1:8) 


0.28 


1.32 


1.00 


0.82 


TZB 0.5 (1:16) 


0.42 


1.62 


1.00 


0.64 


TZB 0.25 (1:32) 


0.47 


1.37 


1.00 


0.64 


TZB 0.125 (1:64) 


0.70 


1.13 


0.92 


1.38 


TZB 0.06(1:128) 


0.69 


1.02 


0.90 


1.06 


TZB 0.03 (1:256) 


1.32 


1.07 


0.92 


0.72 


TZB 0.015(1:512) 


1.62 


1.13 


0.93 


1.48 


PIP alone 


1.92 


5.72 


0.92 


1.23 


Average PEP 
Combined 




1.15±0.25 







The statistics show a very good correlation coefficient for all the fits ahhough the 
MSC is low, indicating that the model may be overparameterized. The values for kp 
increased with decreasing proportion of TZB in the combination. This relationship is in 
agreement with the measured kp values of PIP alone and in combination. The higher the 



108 




Time (h) Time (h) 

Figure 6-4. Curve fit for control (*) and for piperacillin (8 [ig/mL) alone (■) and 
combined with tazobactam: 15 ng/mL (□) , 30 ng/mL (•), 60 ng/mL (O), 
125 n/mL (♦), 250 ng/mL (^), (next page) 500 ng/mL (A), 1 ng/mL (A), 2 
Hg/mL (■), and 4 ^g/mL (□). Error bars indicate SD. 



109 




Figure 6-4. continued 



concentration of TZB in the in vitro model, the longer the half-life of PIP. However, the 
kps determined from simultaneous PK-PD analysis (kpfitted) are higher than the kp 
calculated from measured PIP concentrations. It is known that in Gram-negative bacteria 
the P-lactamases are located in the periplasmic space, between the outer membrane and 
the inner membrane. In opposition to Gram-positive bacteria, no enzyme is present in the 
culture medium. In order to bind to the penicillin binding protein (PBP) located outside 
the inner membrane and to produce the killing effect, piperacillin has to penetrate the 
outer membrane and cross the periplasmic space. It can be postulated that the 
concentration of piperacillin is higher in the medium than inside the periplasm due to the 



110 



presence of the hydrolyzing enzyme. This hypothesis could explain the difference in the 
degradation rate constants measured and fitted if these two spaces are not in rapid 
equilibrium. Most of the ^-lactam agents, including piperacillin and tazobactam, appears 
to penetrate the outer membrane of E. coli by diffusion through porin channels (39, 169). 
It was shown that PIP has a very low permeability in these porin channels due to its bulky 
side chain (39). Hence, the concentration in the periplasmic space is not in rapid 
equilibrium with the concentration outside. It is important to point out that for piperacillin 
alone it seems that the measured outside concentrations were accurate enough to model 
the effect. It may be possible that the presence of TZB interferes with the equilibrium of 
PIP between the medium and the periplasmic space. On the other hand, when TZB is 
present, the activity of the enzymes is decreased and the concentration of PIP in the 
periplasmic space can build up to the necessary levels to produce an effect. This would 
explain the lower EC50S observed for all the cases when PIP is combined with TZB 
compared to when PIP is administered alone. Due to the presence of (3-lactamase, higher 
concentrations of piperacillin are necessary in order to produce the same maximum effect 
obtained with lower concentrations of PIP combined with TZB. 

Simulation of Constant Infusion 

The resuhs of the curve fits for simulations of constant infusions are displayed in 
Figure 6-5. PIP concentrations were not measured in these experiments. The degradation 
rate constants for piperacillin in the different situations were fitted using the 
pharmacodynamic data. The values obtained for EC50 and kp as well as the statistics for 
these fits are shown in Table 6-4. 

Good resuhs were obtained in most of the cases as indicated by the correlation 
coefficients. A direct comparison between the kp obtained in these experiments and those 
obtained in the experiments shown before (PIP 8 ng/mL and combined with various 



Ill 




Figure 6-5. Curve fit for control (*) and piperacillin-tazobactam combinations in 
simulations of constant infijsion. Closed symbols represent PIP-TZB dose 
ratio 1:4 and open symbols represent dose ratio 1:8. PIP 30 mg/h and TZB 
7.5 mg/h (■) or 3.75 mg/h (□), PIP 60 mg/h and TZB 15 mg/h (•) or 7.5 
mg/h (0),(next page) PIP 120 mg/h and TZB 30 mg/h (♦) or 15 mg/h (O), 
PIP 240 mg/h and TZB 60 mg/h (A) or 30 mg/h (A). Error bars indicate 
SD. 



112 




3 10 15 20 25 S 10 IS 20 23 



Time (h) Time (h) 




Time(h) Time(h) 

Figure 6-5. continued 



Table 6-4. Results of curve fits for piperacillin-tazobactam combinations in simulations of 
constant infusion. 



Infusion Rate 


Dose 


Concentration 


kp 


ECso 




MSC 


(mg/h) 


Ratio 


(^g/mL) 


(h-1) 


(Hg/mL) 






PIP 30-TZB 7.5 


1 


4 


PIP 1 - TZB 0.5 


0.35 


0.36 


0.99 


0.77 


PIP 30-TZB 3.75 


1 


8 


PIP 1 - TZB 0.25 


0.37 


0.36 


0.93 


1.57 


PIP 60-TZB 15 


1 


4 


PIP 2 - TZB 1 


0.43 


0.25 


1.00 


0.60 


PIP 60-TZB 7.5 


1 


8 


PIP 2 - TZB 0.5 


0.45 


0.18 


1.00 


0.60 


Pff 120-TZB 30 


1 


4 


PIP 4 - TZB 2 


0.35 


0.42 


1.00 


0.55 


PIP 120-TZB 15 


1 


8 


PIP 4 - TZB 1 


0.43 


0.45 


1.00 


0.60 


PIP 240-TZB 60 


1 


4 


PIP 10 - TZB 4 


0.13 


0.83 


1.00 


0.32 


Pff 240-TZB 30 


1 


8 


PIP 10 - TZB 2 


0.13 


1.81 


1.00 


0.50 



113 



concentrations of TZB) is difficult since the concentrations of PIP changed. For the same 
concentration of TZB different kp values were observed depending on the concentration 
of PIP. The kp for PIP infusion rates between 30 and 120 mg/h with TZB (1 :4 and 1 :8) 
was similar and averaged 0.40 ± 0.05 h"l. The EC50 values obtained were low and 
averaged 0.34 ± 0. 10 ng/mL. The kp and EC50 obtained for the higher infiision rates 
studied (PIP 240 mg/h combined with TZB 30 or 60 mg/h) are similar to the values 
obtained for PIP 8 \xg/mL combined with TZB 2 and 4 ng/mL which was expected since 
the concentrations were similar. 

Simulation of i.v. Multiple Dosing 

In the case of simulations of multiple dosing, the change in piperacillin 
concentration depends both on its dilution (t\/2 = 1 h) and its degradation which depends 
on the respective tazobactam concentration. 

The elimination rate constant used for these experiments was obtained from 
measured PIP concentrations as described in Chapter 5 to be 0.905 h"!. Figures 6-6 
through 6-9 display the results for combinations of PIP-TZB in simulations of i.v. bolus 
multiple dosing. Table 6-5 displays the results of the curve fits for all multiple dose 
studies. 

Very good fits were observed for all the dosing regimens. The correlation 
coefficients and the MSC confirm the appropriateness of the model to describe the 
antiinfective effect of PIP for those experiments. 

The initial concentrations of both drugs used in these sets of experiments were 50 
to 300 times higher than the ones investigated in the infusion simulations. Due to the 
dilution process the degradation of the changing PIP concentration by the p-lactamase is 
affected by the changing TZB concentrations. In the beginning of the dosing interval the 



114 




Figure 6-6. Curve fit for control (A) and piperacillin 2 g (■), 4 g (•), and 8 g (♦ 

combined with tazobactam 0.5 g once a day. Error bars indicate SD. 



115 




10» -j 
10> -j 

lO^* I I I — I — I — I — I — I — I — 1 — 1 — I — I — I— I — I — I — I — I — I I I — I — I— t — 
5 10 15 20 25 

Time (h) 




10»-j 
10' 1 



10" ~J — > — I — I — I — I — I — I — I — I — ( — I — I — I — I — 1 — 1 — 1 — I — I — I — I — I — 1 — I — 
5 10 15 20 25 

Time (h) 




5 10 15 20 25 



Time (h) 



Figure 6-7. Curve fit for control (A) and piperacillin 2 g (■), 4 g (•), and 8 g (♦) 

combined with tazobactam 0.5 g twice a day. Error bars indicate SD. 



116 




5 10 15 20 25 

Time (h) 




3 10 15 20 25 

Time(h) 




5 10 15 20 

Time (h) 



Figure 6-8. Curve fit for control (A) and piperacillin 2 g (■), 4 g (•), and 8 g (♦) 

combined with tazobactam 0.5 g three times a day. Error bars indicate SD. 



117 




5 10 15 20 25 

Time (h) 




5 10 15 20 25 



Time (h) 

;ure 6-9. Curve fit for control (A) and piperacillin 2 g (■), 4 g (•), and 8 g ( 

combined with tazobactam 0.5 g four times a day. Error bars indicate SD. 



118 



Table 6-5. Results of curve fits for i.v. bolus multiple dosing simulations. Piperacillin 2, 4, 
and 8 g (50, 150 and 300 |ag/mL) combined fixed dose of tazobactam 0.5 g (16 
|ig/mL) in all cases. 



Dosing Regimen 


EC50 
(Hg/mL) 


* 

r2 


MSC 


2 g q24h 


1.21 


0.99 


2.84 


4 g q24h 


4.70 


0.99 


3.36 


8 g q24h 


5.04 


0.99 


3.85 


2 g ql2h 


1.94 


0.98 


2.04 


4 g ql2h 


4.39 


0.98 


2.76 


8 g ql2h 


6.31 


1.00 


1.75 


2gq8h 


2.37 


1.00 


0.42 


4 g qsn 


2.44 


1 r\r\ 

1.00 


0.31 


o g qon 


5.40 


1.00 


0.35 


2 g q6h 


1.2/ 


l.UU 


A 00 

0.55 


4 g qon 


4.26 


1 AA 

1.00 


0.74 




7 89 




U.oU 










Average 2 g 


1.70 ±0.56 














Average 4 g 


3.95 ± 1.02 














Average 8 g 


6. 14 ± 1.24 














Average all 


3.93 ±2.09 







concentrations are very high and potentially the enzyme is saturated. In this case 
eventually, the concentration of both drugs is decreased and the degradation rate of PIP 
increases. Although TZB is reported to irreversibly inactivate the hydrolyzing enzyme, 
one has to realize that the bacteria is continuously synthesizing more P-lactamase. With 
decreasing concentrations of TZB, the new enzyme molecules produced can degrade PIP. 
Furthermore, the degradation rate constant calculated for PIP in the i.v. bolus multiple 
dose simulations (0.212 h"!) is the overall rate constant for a non-linear process for one 
dosing interval and cannot be compared to the values obtained when constant 
concentrations are simulated. Finally, the dilution rate process is much more important 



119 



and of greater magnitude than the degradation rate, consequently the changes in PIP 
concentrations are mainly due to the dilution steps rather than to degradation. 

For the simulation of muhiple i.v. bolus administration a fixed dose of TZB (0.5 g) 
was combined with different doses of PIP: 2, 4 and 8 g in order to give dose ratios ranging 
from 1 :4 to 1:16. Although these ratios are based on doses, the actual initial 
concentration ratios in the in vitro system were 1 :3 for PIP 2 g, 1 :9 for PIP 4 g and 1:19 
for Pff 8 g due to the non-linear pharmacokinetics. The EC50 values observed for the 
multiple dose experiments can be grouped according to PIP dose: 1.70 ± 0.56 h"l, 3.95 ± 
1.02 h-1 and 6.14 ± 1.24 h"! for 2, 4 and 8 g, respectively. These differences in EC50 are 
statistically significant (p > 0.05). The EC50 obtained for piperacillin alone in simulation 
of multiple dose studies averaged 5 .72 ng/mL, independent of PIP dose. When PIP 8 g is 
combined with TZB 0.5 g the EC50 is similar to that observed for PIP alone, showing that 
not enough TZB is present in the combination to protect PIP fi-om degradation inside the 
bacteria. Decreasing the proportion of PIP in combination, the EC50 tends to decrease to 
the lower levels obtained for the undiluted concentrations experiments. In other words, 
when the proportion of TZB increases in the combination, higher protection can be 
observed. The potential mechanism for this theory is that PIP competes with TZB for 
binding to the p-lactamase. Studies of the affinity of P-lactam agents to p-lactamases 
reported in the literature are generally performed for a single drug and not for 
combinations (170). No reports about enzyme kinetics for PIP-TZB combinations could 
be found. 

One aspect that has to be emphasized is that all three doses of PIP investigated 
produced very similar effects for the same dosing interval. If the above theory is correct, 
it would imply that an improved effect should be observed when TZB concentrations are 
increased. Therefore, an additional experiment with higher TZB concentrations was 
performed. 



120 



Piperacillin 8 g combined with higher doses of tazobactam (2 and 8 g) was 
analyzed using the proposed model. The elimination rate constant used for these fits was 
0.819 h'l, calculated using measured PIP concentrations in these experiments (Chapter 5), 
The results of the curve fits are shown in Figure 6-10 and the corresponding statistics are 
displayed in Table 6-6. Reasonable fits were obtained in both cases. 




J 10 15 20 25 

Time (h) 




5 10 15 20 25 



Time (h) 

Figure 6-10. Curve fit for control (A) and piperacillin 8 g combined with tazobactam 2 g 
(■) and 4 g (•) twice a day. Error bars indicate SD. 



121 



Table 6-6. Results of the curve fit for piperacillin 8 g (300 ^g/rnL) combined with different 
doses of tazobactam 2 and 8 g (64 and 256 ng/mL) in i.v. bolus muhiple dosing 
simulations. 



Tazobactam dose 


ECso 


r2 


MSC 


(^) 


(ng/mL) 






2 


3,58 


1.00 


6.32 


8 


4.23 


1.00 


6.37 



The comparison of these two PIP-TZB combinations (1:4 and 1:1 dose ratios) 
with the PIP-TZB 1:16 dose ratio shows an increase in the effect for the same PIP dose 
and dosing interval. The increase in TZB levels is reflected in the lower kp (0.819 h"l) m 
comparison to the kp observed for lower TZB concentration (0.905 h'^), showing an 
increase in the protection of PIP. As expected, the EC50 also decreased, from 6.3 1 
lag/mL for the 1:16 for the lower TZB dose to 3.91 ± 0.46 ^g/mL for the higher TZB 
doses. A similar increase in PIP effect with increase in TZB concentration was also 
observed in vivo by Leleu et al. in experimental meningitis in rabbits (171). The increase 
in PIP effect can be partially explained by the higher protection of this drug obtained with 
higher levels of TZB in vitro. Another potentially complicating factor may be a 
pharmacodynamic interaction between PIP and TZB. It has been suggested that weak 
binding by P-lactamase inhibitors (sulbactam) to PBP 2 may potentiate the affinity of the 
piperacillin to PBP 3, its site of action (172). If the same kind of interaction happens with 
TZB, the bactericidal efficiency of piperacillin may consequently be increased. Hence, this 
would explain lower EC50 values for PEP in presence of TZB. It seems that the 
bactericidal activity of PIP-TZB is difficult to explain by considering only a single aspect 
of the interaction between these two drugs and the bacteria. Most probably a combination 
of all factors is involved. What seems to be clear, however, is that sufficiently high 
concentration of tazobactam are necessary to maximize the bactericidal activity of 
piperacillin. 



122 

Conclusions 



An Ejj^ax" n^odel was used to describe the effect of combinations of PIP and TZB 
against E. coli with good results in most cases. It was observed that the addition of TZB 
did not affect the maximum killing effect of PIP (kj^ax)' the k^^gx values obtained in these 
experiments were similar to the ones obtained using piperacillin alone (4). 

In simulations of fluctuating concentrations observed afler i.v. bolus multiple 
dosing the En^ax'^^o^^l proposed was able to describe the effect of PIP alone as well as 
PIP-TZB combinations based on the PIP concentrations determined experimentally. The 
difference observed in the EC50S may be explained by a pharmacokinetic and possibly a 
pharmacodynamic interaction between PIP and TZB. The pharmacokinetic interaction 
will alter the relationship between measured PIP concentrations in the medium and active 
concentration in the periplasmic space dependent on TZB concentration. The 
pharmacodynamic interaction will alter the magnitude of the antiinfective effect for equal 
PIP concentrations at the site of action dependent on TZB concentrations. For the 
experiments using undiluted concentrations, the complex interaction between PIP and 
TZB was more visible. The B^^oc^'^^^^ ^^le to describe the data only when 
simultaneous curve fitting of the pharmacokinetics (kp) and pharmacodynamics (EC50) 
were done. The bactericidal effect of PIP-TZB combinations is possibly the result of 
pharmacokinetic-pharmacodynamic interaction between these two drugs and cannot be 
explained by considering only one aspect individually. However, it seems to be clear that 
sufficiently high concentrations of tazobactam are necessary to maximize the bactericidal 
effect of piperacillin. 

An attempt was made to describe the concentrations of PIP as a function of the 
TZB concentrations for the undiluted experiments. Although it was clear that for a fixed 
concentration of piperacillin the degradation rate constant depends on the TZB 
concentration in the in vitro system, more information is needed in order to use this 



123 



model. A better understanding of the PIP-TZB relationship may be obtained by 
performing a series of experiments simulating constant concentrations of both drugs. In 
one set of experiments a fixed concentration of PIP should be investigated when combined 
with different concentration of TZB. Some experiments with fixed concentration of TZB 
combined with different concentrations of PIP should also be investigated. Piperacillin 
and tazobactam concentrations should be monitored in all experiments. Furthermore, 
concentrations of PIP higher than 8 jig/mL should be investigated with different ratios of 
TZB to determine the relationship between PIP and TZB in a wide range of 
concentrations. Concurrent investigation of the pharmacodynamic effect will also allow us 
to elucidate the relationship between concentrations in the culture medium and at the site 
of action. 



CHAPTER 7 
FINAL CONCLUSIONS 



The pharmacological treatment of infections is still an open field for investigations 
because up to now no satisfactory approaches have been proposed to predict their 
outcomes. A suitable model should incorporate the pharmacokinetics of the antiinfective 
agent and the possibility of changes due to special conditions of the patient, such as renal 
or liver impairment. If the pharmacokinetics can be associated with the pharmacodynamic 
effect of the drug against the infecting agent in a PK-PD model, this will allow 
comparisons of different doses and dose regimens and selection of an optimum treatment 
for a specific patient. In order to devise a PK-PD model the pharmacokinetics of the 
antiinfective agent has to be evaluated at the site of infection. Furthermore, the interaction 
between the antiinfective agent and the bacteria have to be systematically investigated 
under controlled conditions to allow comparisons of doses and dosing intervals. The 
present study was designed to evaluate the pharmacokinetics of piperacillin and 
tazobactam combinations and to investigate the relationship between these concentrations 
and the antiinfective eflfect. The pharmacokinetics of both drugs in different combinations 
was investigated in plasma and tissue in rats. Microdialysis was used to monitor the free 
concentrations in tissue. Predictions of free interstitial concentrations were possible based 
on plasma pharmacokinetics for both drugs. The results were extrapolated to humans. 
Using pharmacokinetics data from the literature, free tissue concentration-time profiles for 
both drugs were predicted and simulated in an in vitro model of infection using E. coli. 
Different doses and dosing regimens were investigated. The change in number of bacteria 
as a function of time was monitored. A pharmacokinetic-pharmacodynamic model 



124 



125 



previously derived for piperacillin alone (4) was used to describe the effect of PEP-TZB 
combinations. The PK-PD model seems to be capable of better predicting the changes in 
number of bacteria for most of the doses and dosing regimens investigated in simulations 
of i.v. bolus administration than other routes of administration investigated. 

The resuhs obtained using the PK-PD model showed a decreased EC50 for 
piperacillin when combined with TZB in comparison to the value obtained when PIP is 
used alone. The decreased concentration necessary to produce 50% of the maximum 
killing effect is a result of pharmacokinetic and possibly a pharmacodynamic effect. 

The pharmacokinetic effect has two distinct aspects which are due to the 
protection of piperaciUin from degradation by the 3-lactamase conferred by tazobactam. 
The higher the concentration of tazobactam in combination, the lower the degradation rate 
of piperacillin. As a resuh, firstly, the inhibition causes longer degradation half-lives of 
PIP in the medium. Secondly, the addition of TZB is likely to change the ratio between 
PIP concentrations in the culture medium and in the periplasmic space. 

The pharmacodynamic interaction also can result in decreased EC50 in the 
presence of TZB compared to the EC50 of PIP alone. Although TZB does not produce 
any killing effect it was suggested that its binding to the PBP may enhance the bactericidal 
effect of piperacillin. 

A comparison between the doses and dosing intervals investigated confirms the 
findings that for P-lactam antibiotics the shorter the dosing interval, the more effect is 
observed. All three dose combinations (PIP 2, 4 and 8 g combined with 0.5 g of TZB) 
were more effective when administered three or four times a day than when administered 
in longer dosing intervals. Three times a day administration is as effective as four times a 
day administration for all the combinations. It can also be concluded that the total daily 
dose can be dramatically reduced by shortening the dosing interval. Piperacillin 2 g 
combined with tazobactam 0.5 g administered four times a day (PIP 8 g and TZB 2 g a 
day) is at least as effective as PIP 8g combined with TZB 2 g administered two times a 



126 



day (PIP 16 g and TZB 4 g a day). The same conclusions were achieved for piperacillin 
alone against an strain ofE. coli non P-lactamase-producer (4). 

It was suggested in the literature that the area under the inhibitory curve (AUIC) is 
a good approach to determine the optimum dose of an antibiotic for the treatment of 
infection. This concept incorporates the pharmacokinetic aspect of the drug (AUC) as 
well as the pharmacodynamic effect (MIC): AUIC = AUC/MIC. An AUIC of 125 h over 
24 h was suggested as a target number (157). This is equivalent to an average 
concentration of five times the MIC. By knowing the MIC of the infecting bacteria and 
the pharmacokinetic characteristics of the drug one could calculate the dose to obtain an 
AUIC of 125 h. This approach was applied to this study. The MIC for piperacillin 
combined with TZB against the E. coli used in the present study was 1 ^g/mL. The 
pharmacokinetic parameters used for piperacillin were shown in Chapter 5. It was 
assumed that sufficient TZB was present in combination at all times to completely inhibit 
the P-lactamase. The doses necessary to produce an AUIC of 125 h were calculated for 
ql2h (1568 mg), q8h (1056 mg), q6h (825 mg) and a constant infiision (128 mg/h) over 
24 h. These doses were used to predict the free concentrations in tissue expected for each 
dosing interval. The resulting concentrations were simulated in our Ej^^x'^^odel to 
determine the bactericidal effect. The parameters used for the simulations were: k of 1 .54 
h"l, kmax of 3.87 h'^ The EC50 was calculated based on the linear relationship between 
this concentration and the MIC, as shown for piperacillin alone (173). Based on an MIC 
of 1 ng/mL the resultant EC50 is 2. 1 |jg/mL. The initial inoculum was 5 xlO^ CFU/mL. 
Figure 7-1 shows PIP concentration-time profiles used for the simulations. The results of 
the simulations of the bactericidal effect are displayed in Figure 7-2. 

Since all four dosing regimens were calculated to produce the same AUIC target 
value they should be equipotent. This is contrary to the results shown in Figure 7-2. The 
shorter the dosing interval the more pronounced is the effect. For the doses predicted 
from the AUIC approach only the constant infusion produced a significant effect 



127 




Time (h) 



SO 



10 



"ES. 



Time (h) 



— 1 — 

20 



c 

o 



8 

a 

d 




Time(h) 



Figure 7-1. Free tissue concentration-time profiles of piperacillin 1568 mg ql2h (long 
dashed line), 1056 mg q8h (medium dashed line), 825 mg q6h (short dashed 
line), and steady-state concentration for a constant infusion of 128 mg/h over 
24 h (solid line). 



over 24 hours. Three conclusions can be drawn fi-om this. First, the AUIC is a very 
simplistic approach to predict the bactericidal effect of an antibiotic. Difference in the 
dosing regimens are not reflected in the final AUIC value but produce a significant impact 
in the antiinfective effect. Second, the E^ax" model is a more detailed approach to 
compare doses and dosing regimens. Finally, as it was shown before in our experiments, 
for P-lactam antibiotics the shorter the dosing interval the more effective the bactericidal 
effect of the same total dose. If the main concern is to reduce the doses of PIP-TZB 



128 




Figure 7-2. Simulations of PIP-TZB effect expected with doses calculated to give an 
AUIC of 125 h"l for different dosing intervals: 1568 mg ql2h (long dashed 
line), 1056 mg qSh (medium dashed line), 825 mg q6h (short dashed line) and 
constant infusion (128 mg/h) over 24 h (solid line). 



combination, a shorter dosing interval should be used. The downside of this approach is 
poor patient and health provider compliance. 

One of the goals of the study was to show that PIP-TZB combination can be 
administered twice a day whhout loss of efficacy. Based on the results of these 
experiments two times a day administration does not seem advisable for PIP 2, 4 or 8 g 
when combined with 0.5 g of TZB. However, the results suggest that an increase in TZB 
dose is followed by an increase in the effect of a fixed dose of PIP. Piperacillin 8 g 
combined with TZB 2 g ql2h is more effective than PIP 8 g combined with TZB 0.5 g for 



129 



the same dosing interval. Lower doses of PIP combined with higher doses of TZB should 
show the same trend and should be investigated. It should be kept in mind that in vivo the 
observed effect will be greater due to the additional immunological component. It seems 
to be reasonable to conclude that if longer dosing intervals for PIP-TZB combinations are 
to be used, the dose of TZB has to be increased. 

Another way to compare the different doses and dosing regimens is by analyzing 
the number of bacteria remaining in the in vitro system after 24 h. If the number decreases 
compared to the initial inoculum, effective killing took place and a positive effect was 
obtained. If the number of bacteria is similar or higher than the initial inoculum an overall 
negative effect can be assumed. Table 7-1 shows the fraction of bacteria remaining in the 
in vitro system after 24 h for the different dosing regimens investigated. 



Table 7-1. Magnitude of antiinfective activity based on the number of bacteria remaining 
in the in vitro system after 24 h in comparison to the initial inoculum. 



Dosing Interval 


PIP2g/ 
TZB 0.5 g 


PIP4g/ 
TZB 0.5 g 


PIP 8g/ 
TZB 0.5 g 


PIP8g/ 
TZB 2 g 


PIP8g/ 
TZB 8g 


q6h 


-H- 


++ 


++ 






q8h 


+ 


++ 


++ 






ql2h 








+ 


+ 


q24h 













(++) fraction < 0.01; (+) between 0.01 and 1; (-) between 1 and 100; (-) > than 100. 
blank space = not determined 



For all three PLP doses combined with TZB 0.5 g an increased effect is observed 
with decreasing the dosing interval. For these combinations the dosing regimens ql2h and 
q24h produced negative results. For a fixed dose of TZB (0.5 g), PIP 4 and 8 g 
administered three times a day and PIP 2, 4 and 8 g administered four times a day, astrong 
bactericidal effect was produced. For the ql2h dosing interval doses of 2, 4, and 8 g of 
PIP with 0.5 g of TZB did not produce an overall bactericidal effect. Only if the TZB 



130 



dose was increased to 2 and 8 g, was a positive effect observed. This could allow for an 
increase in the dosing interval from three to two times a day for PIP-TZB combinations. 
The importance of using enough TZB in combination in order to maximize the effect of 
PIP has to be considered when devising doses and dosing regimens for this combination. 

The results obtained in this work have to be viewed as an initial attempt to 
describe the antiinfective effect of PIP-TZB combinations. Many questions have to be 
answered in order to obtain a more comprehensive model to predict effects of other 
combinations not evaluated in this study. In addition to a better understanding of the 
complex interaction between these two drugs and the Gram-negative bacteria, another 
factor related to the pharmacokinetics of this combination in infected tissues has to be 
evaluated. The basic assumption for this study was that the plasma data can be used to 
predict free tissue concentrations at the site of infection. The assumption was validated in 
non-infected animals and extrapolated to humans. A precise simulation of the predicted 
concentrations in the in vitro model was not possible due to the presence of P-lactamase 
which degraded PIP. Hence, the half-lives obtained in the model were shorter than those 
predicted from the dilution alone. Whether or not this effect is also observed at the site of 
infection in vivo is a question for investigation. If different pharmacokinetic profiles are 
observed in infected tissue for PIP and/or TZB, adjustments will have to be made in order 
to predict these levels based on plasma data. The determination of free concentrations of 
PIP and TZB in infected tissue by microdialysis could answer this question and further 
elucidate the pharmacokinetics and pharmacodynamic aspects of this combination. 

Applying these results to the clinical situation has to be done with great care. The 
bacterial grov^h in vitro and in vivo are different and consequently the antiinfective 
bactericidal effect is different in these two environments. It was also observed in this 
study that piperacillin pharmacokinetics in vitro against a |3-lactamase producing bacteria 
differs from the expected patterns due to degradation. If this effect is also significant at 
the infection site in vivo still has to be investigated. The in vitro model of infection does 



131 



not account for the contribution of the immune system of the immune-competent host. 
Consequently the pharmacodynamic effect observed in vitro is probably amplified in vivo. 
In spite of all the differences observed in vivo and in vitro the Eu^ax-n^odel allows for 
systematic comparison of different doses and dosing regimens and for prediction of the 
most efficacious ones. Ultimately the findings will need to be confirmed in clinical trials. 



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BIOGRAPHICAL SKETCH 



Teresa Cristina Tavares Dalla Costa was bom on October 9, 1962, to Dario Dalla 
Costa and Ligia Maria Tavares Dalla Costa. She entered Pharmacy School at the 
Universidade Federal do Rio Grande do Sul - UFRGS in Porto Alegre (RS), Brazil in 
1980 and graduated in 1984. She entered the graduate school in March 1986 and 
graduated from the same University with a degree of Master of Science in December 
1990. She accepted a position as Assistant Professor in the Department of Production and 
Control of Medicines in the College of Pharmacy of the UFRGS in December 1989. Upon 
coming to the United States in August 1992 she entered graduate school in the College of 
Pharmacy at the University of Florida. She worked under the supervision of Dr. Hartmut 
Derendorf 

The author received her Doctor of Philosophy degree in the pharmacy in August 

1996. 



147 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fiilly adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 

Hartmut Derendorf, Chair 
Professor of Pharmaceutics 

I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. r>vw 

Guenther Hochhaus 

Associate Professor of Pharmaceutics 

I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philosophy. 




Gayle Brazeau 
Assistant Professor of Pharmaceutics 



I certify that I have read this study and that in my opinion it conforms to 
acceptable standards of scholarly presentation and is fully adequate, in scope and quality, 
as a dissertation for the degree of Doctor of Philo/ophy. 




Kenneth Rand 
Professor of Pathology and Laboratory 
Medicine 



This dissertation was submitted to the Graduat^ Faculty of the College of 
Pharmacy and to the Graduate School and was accented as partial fulfillment^(?fti)e 
requirements for the degree of Doctor of Philosopl 

August, 1996 




Dean, College of Pharmacy 



Dean, Graduate School